http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Jkoh35Physics Book - User contributions [en]2026-05-05T11:53:43ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7198Leonhard Euler2015-12-02T01:11:48Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables.<br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>K L</math> is the length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
* http://eulerarchive.maa.org/pages/E088.html ''Nova theoria lucis et colorum''<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7192Leonhard Euler2015-12-02T01:08:13Z<p>Jkoh35: /* Work in Astronomy */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables.<br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>K L</math> is the length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7191Leonhard Euler2015-12-02T01:07:33Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>K L</math> is the length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7178Leonhard Euler2015-12-02T01:04:47Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>K L</math> is the length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7175Leonhard Euler2015-12-02T01:04:10Z<p>Jkoh35: /* Structural Engineering */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>K L</math> is the length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7163Leonhard Euler2015-12-02T01:02:18Z<p>Jkoh35: /* References */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
* Weisstein, Eric W. "Euler's Equations of Inviscid Motion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EulersEquationsofInviscidMotion.html<br />
* "The Euler-Bernoulli Beam." (2005): 368-401. Center for Aerospace Structures. University of Colorado Boulder, 2005. Web. 1 Dec. 2015.<br />
* Grieve, David J. "Euler Buckling Formula Derivation." Euler Buckling Formula Derivation. Plymouth University, 1 Mar. 2004. Web. 01 Dec. 2015.<br />
* Musielak, Dora. "Euler: Genius Blind Astronomer Mathematician." (n.d.): n. pag. ArXiv.org. Cornell University Library, 28 June 2014. Web. 1 Dec. 2015.<br />
<br />
[[Category:Notable Scientists]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7150Leonhard Euler2015-12-02T00:59:42Z<p>Jkoh35: /* External links */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
* http://web.mit.edu/16.unified/www/SPRING/materials/Lectures/M4.7-Unified09.pdf Euler's Column Formula<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7146Leonhard Euler2015-12-02T00:57:51Z<p>Jkoh35: /* Structural Engineering */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering, commonly referred to as Euler's Column Formula.<br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7126Leonhard Euler2015-12-02T00:46:35Z<p>Jkoh35: /* External links */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
* http://eulerarchive.maa.org/ A digital library dedicated to the work and life of Leonhard Euler<br />
* http://micro.magnet.fsu.edu/optics/timeline/people/euler.html Euler's work on optics <br />
* https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html Euler's Wave Theory of Light<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7115Leonhard Euler2015-12-02T00:39:08Z<p>Jkoh35: /* Further reading */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* Dunham, William. <i>Euler: The Master of Us All</i>. Washington, D.C.: Mathematical Association of America, 1999. Print.<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7112Leonhard Euler2015-12-02T00:37:28Z<p>Jkoh35: /* See also */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
* [[Daniel Bernoulli]]<br />
* [[Wave-Particle Duality]]<br />
* [[Young's Modulus]]<br />
* [[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* {{cite book |authorlink=William Dunham (mathematician) |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://books.google.com/books?id=uKOVNvGOkhQC |year=1999 |publisher=Mathematical Association of America |isbn=978-0-88385-328-3 |ref=harv}}<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7110Leonhard Euler2015-12-02T00:36:58Z<p>Jkoh35: /* See also */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
[[Daniel Bernoulli]]<br />
<br />
[[Wave-Particle Duality]]<br />
<br />
[[Young's Modulus]]<br />
<br />
[[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* {{cite book |authorlink=William Dunham (mathematician) |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://books.google.com/books?id=uKOVNvGOkhQC |year=1999 |publisher=Mathematical Association of America |isbn=978-0-88385-328-3 |ref=harv}}<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7109Leonhard Euler2015-12-02T00:36:35Z<p>Jkoh35: /* See also */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
[[Daniel Bernoulli]]<br />
<br />
<br />
[[Wave-Particle Duality]]<br />
<br />
<br />
[[Young's Modulus]]<br />
<br />
<br />
[[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* {{cite book |authorlink=William Dunham (mathematician) |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://books.google.com/books?id=uKOVNvGOkhQC |year=1999 |publisher=Mathematical Association of America |isbn=978-0-88385-328-3 |ref=harv}}<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7108Leonhard Euler2015-12-02T00:36:12Z<p>Jkoh35: /* Further reading */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
[[Daniel Bernoulli]]<br />
[[Wave-Particle Duality]]<br />
[[Young's Modulus]]<br />
[[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* {{cite book |authorlink=William Dunham (mathematician) |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://books.google.com/books?id=uKOVNvGOkhQC |year=1999 |publisher=Mathematical Association of America |isbn=978-0-88385-328-3 |ref=harv}}<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7107Leonhard Euler2015-12-02T00:35:18Z<p>Jkoh35: /* Further reading */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
[[Daniel Bernoulli]]<br />
[[Wave-Particle Duality]]<br />
[[Young's Modulus]]<br />
[[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
* {{cite book |authorlink=William Dunham (mathematician) |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://books.google.com/books?id=uKOVNvGOkhQC |year=1999 |publisher=Mathematical Association of America}}<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7094Leonhard Euler2015-12-02T00:29:28Z<p>Jkoh35: /* See also */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
[[Daniel Bernoulli]]<br />
[[Wave-Particle Duality]]<br />
[[Young's Modulus]]<br />
[[Multisource Interference: Diffraction]]<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7071Leonhard Euler2015-12-02T00:23:23Z<p>Jkoh35: /* Structural Engineering */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, depending on the conditions of end support of the column<br />
:<math>K L</math> = length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7068Leonhard Euler2015-12-02T00:22:13Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>{ \mathbf {u}}</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7064Leonhard Euler2015-12-02T00:20:33Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>u</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>\rho\</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=7060Leonhard Euler2015-12-02T00:19:25Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and he entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
where<br />
:<math>w</math> = Out-of-plane displacement of the beam <br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia, and<br />
:<math>q</math> = distributed load (force per unit length)<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
where<br />
:<math>u</math> = fluid velocity<br />
:<math>p</math> = pressure, and<br />
:<math>rho</math> = fluid density<br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6239Leonhard Euler2015-12-01T19:25:17Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6233Leonhard Euler2015-12-01T19:24:02Z<p>Jkoh35: /* Contributions to Physics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “<math>e</math>”, the concept of a function, summation notation “Σ”, imaginary unit notation “<math>i</math>”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6230Leonhard Euler2015-12-01T19:23:06Z<p>Jkoh35: /* Contributions to Physics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “{{math|<var>e</var>}}”, the concept of a function, summation notation “Σ”, imaginary unit notation “{{math|<var>i</var>}}”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6223Leonhard Euler2015-12-01T19:21:36Z<p>Jkoh35: /* Contributions to Physics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “{{mvar|e}}”, the concept of a function, summation notation “Σ”, imaginary unit notation “{{math|<var>i</var>}}”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6215Leonhard Euler2015-12-01T19:19:31Z<p>Jkoh35: /* Contributions to Physics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|<var>i</var>}}”, and popularizing <math title="pi">\pi</math>; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6204Leonhard Euler2015-12-01T19:17:21Z<p>Jkoh35: /* Contributions to Physics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|<var>i</var>}}”, and popularizing “/pi”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6200Leonhard Euler2015-12-01T19:15:58Z<p>Jkoh35: /* Work in optics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light.<br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6196Leonhard Euler2015-12-01T19:15:07Z<p>Jkoh35: /* Structural Engineering */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical force (vertical load on column),<br />
:<math>E</math> = modulus of elasticity (Young's Modulus),<br />
:<math>I</math> = area moment of inertia,<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6192Leonhard Euler2015-12-01T19:14:04Z<p>Jkoh35: /* Further reading */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical [[force]] (vertical load on column),<br />
:<math>E</math> = [[modulus of elasticity]],<br />
:<math>I</math> = [[area moment of inertia]],<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
http://www.colorado.edu/engineering/CAS/courses.d/AVMM.d/AVMM.Ch08.d/AVMM.Ch08.pdf<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6187Leonhard Euler2015-12-01T19:13:30Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
:<math>\frac{\mathrm{d}^2}{\mathrm{d} x^2}\left(EI \frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\right) = q\,</math><br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In ''Nova theoria lucis et colorum'' (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
:<math>F=\frac{\pi^2 EI}{(KL)^2}</math><br />
<br />
where<br />
:<math>F</math> = maximum or critical [[force]] (vertical load on column),<br />
:<math>E</math> = [[modulus of elasticity]],<br />
:<math>I</math> = [[area moment of inertia]],<br />
:<math>L</math> = unsupported length of column,<br />
:<math>K</math> = column effective length factor, whose value depends on the conditions of end support of the column, as follows.<br />
::For both ends pinned (hinged, free to rotate), <math>K = 1.0</math>.<br />
::For both ends fixed, <math>K = 0.50</math>.<br />
::For one end fixed and the other end pinned, <math>K = 0.699\ldots</math>.<br />
::For one end fixed and the other end free to move laterally, <math>K = 2.0</math>.<br />
:<math>K L</math> is the effective length of the column.<br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6159Leonhard Euler2015-12-01T19:03:57Z<p>Jkoh35: /* Fluid Dynamics */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \mathbf {u}}\cdot\nabla<br />
\right){ \mathbf {u}}+\nabla p=0<br />
</math><br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6157Leonhard Euler2015-12-01T19:02:44Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{ \bold {u}}\cdot\nabla<br />
\right){ \bold {u}}+\nabla p=0<br />
</math><br />
<br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6155Leonhard Euler2015-12-01T19:01:55Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (Inviscid flow) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{\bold {u}}\cdot\nabla<br />
\right){\bold {u}}+\nabla p=0<br />
</math><br />
<br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6114Leonhard Euler2015-12-01T18:47:49Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity ([[Inviscid flow]]) that are now known as the Euler Equations. <br />
<br />
:<math><br />
\rho\left(<br />
\frac{\partial}{\partial t}+{\bold u}\cdot\nabla<br />
\right){\bold u}+\nabla p=0<br />
</math><br />
<br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6109Leonhard Euler2015-12-01T18:45:48Z<p>Jkoh35: /* Further reading */</p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://eulerarchive.maa.org/<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6104Leonhard Euler2015-12-01T18:44:24Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
<br />
[[File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object ''appears'' to have moved in front of the red square.]]<br />
<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
http://arxiv.org/ftp/arxiv/papers/1406/1406.7397.pdf<br />
http://blog.mechguru.com/machine-design/how-to-apply-the-euler-bernoulli-beam-theory-for-beam-deflection-calculation/<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6089Leonhard Euler2015-12-01T18:37:14Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[Sigma|Σ]”, imaginary unit notation “{{math|''bi''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
<br />
[[File:Laser Interference.JPG|thumb|Diffraction pattern of red [[laser]] beam made on a plate after passing a small circular hole in another plate]]<br />
<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
http://micro.magnet.fsu.edu/optics/timeline/people/euler.html<br />
https://muse.jhu.edu/journals/perspectives_on_science/v016/16.4.pedersen.html<br />
<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6072Leonhard Euler2015-12-01T18:30:08Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. <br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “[[Sigma|Σ]]”, imaginary unit notation “{{math|''i''}}”, and popularizing “<ref name="pi">”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
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This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6054Leonhard Euler2015-12-01T18:24:12Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
[[File:Leonhard Euler.jpg|200px|thumb|right|Leonhard Euler]]<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. Euler was an important influence to Pierre-Simon Laplace.<br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “sigma”, imaginary unit notation “I”, and popularizing “I”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6050Leonhard Euler2015-12-01T18:22:35Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
{{Infobox scientist<br />
|name = Leonhard Euler<br />
|image = Leonhard Euler.jpg<br />
|image_size = 220px<br />
|caption = Portrait by [[Jakob Emanuel Handmann]] (1753)<br />
|birth_date = {{birth date|1707|4|15|df=y}}<br />
|birth_place = [[Basel]], [[Old Swiss Confederacy|Switzerland]]<br />
|death_date = {{death date and age|1783|9|18|1707|4|15|df=y}}<br/><small><nowiki>[</nowiki>[[Old Style and New Style dates|OS]]: 7 September 1783<nowiki>]</nowiki></small><br />
|death_place = [[Saint Petersburg]], [[Russian Empire]]<br />
|residence = [[Kingdom of Prussia]], Russian Empire<br> Switzerland<br />
|field = Mathematics and [[physics]]<br />
|work_institutions = [[Russian Academy of Sciences|Imperial Russian Academy of Sciences]]<br>[[Prussian Academy of Sciences|Berlin Academy]]<br />
|alma_mater = [[University of Basel]]<br />
|doctoral_advisor = [[Johann Bernoulli]]<br />
|doctoral_students = [[Nicolas Fuss]]<br>[[Johann Hennert]]<br>[[Stepan Rumovsky]]<br />
|notable_students = [[Joseph Louis Lagrange]]<br />
|known_for = [[List of topics named after Leonhard Euler|See full list]]<br />
|prizes =<br />
|religion = [[Calvinism|Calvinist]]<ref name=graves>{{cite book|title=Scientists of Faith|author=Dan Graves|location=Grand Rapids, MI|year=1996|publisher=Kregel Resources|pages=85–86}}</ref><ref name=bell>{{cite book|title=Men of Mathematics, Vol. 1|author=E. T. Bell|location=London|year=1953|publisher=Penguin|page=155}}</ref><br />
|footnotes = He is the father of the mathematician [[Johann Euler]].<br />He is listed by an academic genealogy as the equivalent to the doctoral advisor of Joseph Louis Lagrange.<ref name=mathg/><br />
|signature = Euler's signature.svg<br />
}}<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. Euler was an important influence to Pierre-Simon Laplace.<br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “sigma”, imaginary unit notation “I”, and popularizing “I”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=6042Leonhard Euler2015-12-01T18:19:41Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
==Overview==<br />
<br />
Leonhard Euler was a Swiss Mathematician and physicist who made important contributions to math and physics. Euler is often considered one of the greatest mathematicians to have ever lived. Euler was an important influence to Pierre-Simon Laplace.<br />
<br />
==Early Life==<br />
<br />
Euler was born in Basel, Switzerland on April 15th, 1707. His father was a minister and the family naturally expected Euler to also go in to ministry. However, his father sparked a curiosity in math for Euler and Euler entered University of Basel at the age of 14, with Johann Bernoulli as his mentor.<br />
<br />
==Contributions to Physics==<br />
<br />
Arguably the greatest mathematician in history, Euler made lots of contribution to math such as the number “e”, the concept of a function, summation notation “sigma”, imaginary unit notation “I”, and popularizing “I”; however, Euler also made lots of important contributions to physics. <br />
<br />
===Euler-Bernoulli beam equation===<br />
The theory validates the beam deflection calculation for laterally loaded beams. The equation provides a relationship between the deflection of the beam and the applied load intensity. <br />
<br />
===Work in Astronomy===<br />
<br />
====Understanding the nature of comets====<br />
In addition to his work with classical mechanics, Euler was recognized by Paris Academy Prizes over the course of his career for calculating, with great accuracy, the orbits of comets and other celestial bodies. <br />
<br />
====Calculating the parallax of the sun====<br />
Euler calculated the parallax of the sun, calculating the difference in the apparent position of the object and the actual position of the object. Euler’s calculation of the parallax later led to the development of more accurate longitude tables. <br />
<br />
===Work in optics===<br />
While Newton argued that light was made of particles, Euler argued that light behaved more like waves. In Nova theoria lucis et colorum (1746), Euler argued that diffractions can be more easily argued with the wave theory rather than the previous “pulse theory”. Euler’s wave theory remained the dominant theory about light until the quantum theory of light. <br />
<br />
===Structural Engineering===<br />
Euler also published a formula for calculating the force where the strut would fail that is often used in structural engineering. <br />
<br />
===Fluid Dynamics===<br />
Euler in 1757 published a set of equations for flow of an ideal fluid with no viscosity (inviscid flow) that are now known as the Euler Equations. <br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=4852Leonhard Euler2015-11-30T21:49:46Z<p>Jkoh35: </p>
<hr />
<div>by Jong Rak Koh<br />
<br />
==Path Independence==<br />
<br />
The potential difference between two locations does not depend on the path taken between the locations chosen. <br />
<br />
===A Mathematical Model===<br />
<br />
In order to find the potential difference between two locations, we use this formula <math> dV = -\left(E_x*dx + E_y*dy + E_z*dz\right) </math>, where '''E''' is the electric field with components in the x, y, and z directions. Delta x, y, and z are the components of final location minus to the components of the initial location.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Leonhard_Euler&diff=4825Leonhard Euler2015-11-30T21:40:48Z<p>Jkoh35: Created page with "by Elisa Mercando ==Path Independence== The potential difference between two locations does not depend on the path taken between the locations chosen. ===A Mathematical M..."</p>
<hr />
<div>by Elisa Mercando <br />
<br />
==Path Independence==<br />
<br />
The potential difference between two locations does not depend on the path taken between the locations chosen. <br />
<br />
===A Mathematical Model===<br />
<br />
In order to find the potential difference between two locations, we use this formula <math> dV = -\left(E_x*dx + E_y*dy + E_z*dz\right) </math>, where '''E''' is the electric field with components in the x, y, and z directions. Delta x, y, and z are the components of final location minus to the components of the initial location.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
=Simple Example=<br />
[[File:pathindependence.png]]<br />
<br />
In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>. <br />
<br />
Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1</math><br />
<br />
[[File:BC.png]]<br />
<br />
Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C. <br />
<br />
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.<br />
<br />
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.<br />
<br />
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jkoh35http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=4823Main Page2015-11-30T21:40:12Z<p>Jkoh35: /* Notable Scientists */</p>
<hr />
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* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Categories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
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===Interactions===<br />
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*[[Kinds of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
*[[Newton's Second Law of Motion]]<br />
*[[Newton's Third Law of Motion]]<br />
*[[Gravitational Force]]<br />
*[[Terminal Speed]]<br />
*[[Simple Harmonic Motion]]<br />
*[[Speed and Velocity]]<br />
*[[Electric Polarization]]<br />
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===Theory===<br />
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*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[Big Bang Theory]]<br />
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===Notable Scientists===<br />
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*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Joseph Henry]]<br />
*[[Michael Faraday]]<br />
*[[J.J. Thomson]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
*[[Oliver Heaviside]]<br />
*[[Rosalind Franklin]]<br />
*[[Erwin Schrödinger]]<br />
*[[Enrico Fermi]]<br />
*[[Robert J. Van de Graaff]]<br />
*[[Charles de Coulomb]]<br />
*[[Hans Christian Ørsted]]<br />
*[[Philo Farnsworth]]<br />
*[[Niels Bohr]]<br />
*[[Georg Ohm]]<br />
*[[Galileo Galilei]]<br />
*[[Gustav Kirchhoff]]<br />
*[[Max Planck]]<br />
*[[Heinrich Hertz]]<br />
*[[Edwin Hall]]<br />
*[[James Watt]]<br />
*[[Count Alessandro Volta]]<br />
*[[Josiah Willard Gibbs]]<br />
*[[Richard Phillips Feynman]]<br />
*[[Sir David Brewster]]<br />
*[[Daniel Bernoulli]]<br />
*[[William Thomson]]<br />
*[[Leonhard Euler]]<br />
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===Properties of Matter===<br />
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*[[Mass]]<br />
*[[Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Density]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
*[[Heat Capacity]]<br />
*[[Specific Heat]]<br />
*[[Wavelength]]<br />
*[[Conductivity]]<br />
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===Contact Interactions===<br />
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* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Compression or Normal Force]]<br />
* [[Length and Stiffness of an Interatomic Bond]]<br />
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===Momentum===<br />
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* [[Vectors]]<br />
* [[Kinematics]]<br />
* [[Conservation of Momentum]]<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Impulse Momentum]]<br />
* [[Curving Motion]]<br />
* [[Multi-particle Analysis of Momentum]]<br />
* [[Iterative Prediction]]<br />
* [[Newton's Laws and Linear Momentum]]<br />
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===Angular Momentum===<br />
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* [[The Moments of Inertia]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
* [[Right Hand Rule]]<br />
* [[Angular Velocity]]<br />
* [[Predicting a Change in Rotation]]<br />
* [[Conservation of Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[Total Angular Momentum]]<br />
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===Energy===<br />
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*[[The Energy Principle]]<br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
*[[Spring Potential Energy]]<br />
*[[Internal Energy]]<br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Franck-Hertz Experiment]]<br />
*[[Power]]<br />
*[[Energy Graphs]]<br />
*[[Air Resistance]]<br />
*[[Electronic Energy Levels]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Specific Heat Capacity]]<br />
*[[Quantized Energy Levels]]<br />
*[[Energy Density]]<br />
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===Collisions===<br />
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*[[Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
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===Fields===<br />
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* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
** [[Charged Cylinder]]<br />
**[[A Solid Sphere Charged Throughout Its Volume]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Potential Difference of point charge in a non-Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
**[[Potential Difference in an Insulator]]<br />
**[[Energy Density and Electric Field]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
*[[Charge Motion in Metals]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Magnetic Field of a Long Straight Wire]]<br />
**[[Magnetic Field of a Loop]]<br />
**[[Magnetic Field of a Solenoid]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Biot-Savart Law for Currents]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
**[[Moving Point Charge]]<br />
**[[Non-Coulomb Electric Field]]<br />
**[[Motors and Generators]]<br />
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===Simple Circuits===<br />
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*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
*[[Ohm's Law]]<br />
*[[Series Circuits]]<br />
*[[RC]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
*[[Surface Charge Distributions]]<br />
*[[Feedback]]<br />
*[[Transformers]]<br />
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===Maxwell's Equations===<br />
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*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Ampere's Law]]<br />
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Faraday's Law]]<br />
**[[Curly Electric Fields]]<br />
**[[Inductance]]<br />
**[[Lenz's Law]]<br />
***[[Lenz Effect and the Jumping Ring]]<br />
**[[Motional Emf using Faraday's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
**[[Superconducters]]<br />
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===Radiation===<br />
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*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
*[[Lenses]]<br />
*[[Energy and Momentum Analysis in Radiation]]<br />
*[[Electromagnetic Propagation]]<br />
*[[Snell's Law]]<br />
*[[Light Propagation Through a Medium]]<br />
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===Sound===<br />
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*[[Doppler Effect]]<br />
*[[Nature, Behavior, and Properties of Sound]]<br />
*[[Resonance]]<br />
*[[Sound Barrier]]<br />
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*[[blahb]]<br />
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== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Jkoh35