Beauty of Equations?

[Gerald H]

Article from today's Guardian:

https://www.theguardian.com/science/2016...-beautiful

Note error in quiz.

Any candidates for attractive equations?

[Ángel Martin]

Attractive they may not be but to me the superb pinnacle is captured by the Maxwell equations, followed shortly by the Navier-Stokes equations... this is of course just a personal bias.

[BruceH]

(11-21-2016 12:14 PM)Gerald H Wrote:  Note error in quiz.

Oh yes, well spotted. Everyone knows that it should be \(e^{i\tau} = 1\)
;-)

[JurgenRo]

(11-21-2016 01:26 PM)Ángel Martin Wrote:  Attractive they may not be but to me the superb pinnacle is captured by the Maxwell equations, followed shortly by the Navier-Stokes equations... this is of course just a personal bias.

Agreed! Even though Nature seems to be nonlinear, Electrodynamics is fully captured by the pure linear Maxwell Equations. Also, The Navier-Stokes Equations of Fluid Dynamics are "just" seminlinear. However, the proof of the global existence and uniqueness of smooth solutions to the 3D Navier-Stokes Equation is still lacking, it's a Millenium-Problem! Long time ago I did my math. PhD Thesis on timewise Approximation of the Stokes-Equations (which is the Navier-Stokes without convecive term and thus it is linear). Learned to love this set of Equations! Has been exciting years :-)

[Gerald H]

Here's a film of Hannah Fry's choice:

https://www.theguardian.com/science/vide...axies-form

[JurgenRo]

(11-22-2016 05:25 PM)Gerald H Wrote:  Here's a film of Hannah Fry's choice:

https://www.theguardian.com/science/vide...axies-form

Great! Thanks for sharing!! :-)

[Jeff O.]

(11-21-2016 05:10 PM)BruceH Wrote:  

(11-21-2016 12:14 PM)Gerald H Wrote:  Note error in quiz.

Oh yes, well spotted. Everyone knows that it should be \(e^{i\tau} = 1\)
;-)

I think that would be \(e^{i\tau/2} = -1\), (or preferably, \(e^{i\tau/2} + 1 = 0\)), which kinda sorta shows why tau is wrong, i.e., messes up Euler's identity.

[Santi]

I've always felt attracted to transcendental calculations, so I choose:

M=E-e*sin(E)