Undergrad On spherical geometry and its applications in physics

[trees and plants]

Hello. Questions: do you know any applications of spherical geometry in physics? Are there any relations between spherical geometry and hyperbolic geometry? Why does Riemannian geometry use sphere theorems so much? Thank you.

 

[jedishrfu]

Acoustics uses both spherical and cylindrical coordinates in a lot of examples from round drumheads to underwater sound propagation to sound propagation on the solar surface and the list goes on...

It is a worthwhile endeavor to get familiar with them and how they are used in practical problems in classical and quantum mechanical systems.

I suspect spherical geometry comes into play as an example where RiemannIan Geometry concepts can be easily tested. The same goes for hyperbolic geometry.

 

[brainpushups]

The original application was for astronomy. There's a book called Heavenly Mathematics which I enjoyed working through recently. It traces the historical development of the math of spherical trig which I found insightful for understanding the formulas you may have seen. One of the applications, just to give an example, is to determine the amount of daylight at a given latitude for a particular day of the year. Of course, now you could just google it!