On spherical geometry and its applications in physics
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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.
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.
The original application was for astronomy. There's a book called Heavenly Mathematicswhich 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!