On spherical geometry and its applications in physics

In summary, spherical geometry is used in a variety of fields, including acoustics and astronomy. It is also closely related to Riemannian and hyperbolic geometry. The original application of spherical geometry was in astronomy, but it has practical applications in determining daylight and other calculations.
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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.
 
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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.
 
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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!
 
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1. What is spherical geometry?

Spherical geometry is a type of geometry that studies the properties of shapes and figures on the surface of a sphere. It is a non-Euclidean geometry, meaning that it does not follow the same rules and axioms as traditional Euclidean geometry.

2. How is spherical geometry used in physics?

Spherical geometry has many applications in physics, particularly in the fields of astronomy and geophysics. It is used to model the curvature of the Earth's surface and to calculate distances and angles on the surface of a sphere. It is also used in celestial mechanics to study the motion of objects in space.

3. What are some real-world examples of spherical geometry?

Spherical geometry is used in many real-world applications, such as navigation systems, mapping the Earth's surface, and predicting the movement of celestial bodies. It is also used in the design of satellite orbits and in the study of gravitational fields.

4. How does spherical geometry differ from Euclidean geometry?

Unlike Euclidean geometry, which is based on flat surfaces, spherical geometry is based on the surface of a sphere. This means that the rules and properties of shapes and figures are different in spherical geometry. For example, the angles of a triangle in spherical geometry will add up to more than 180 degrees, whereas in Euclidean geometry they will always add up to 180 degrees.

5. What are some challenges of working with spherical geometry?

One of the main challenges of working with spherical geometry is that it is not as intuitive as Euclidean geometry. This can make it difficult to visualize and understand certain concepts. Additionally, calculations in spherical geometry can be more complex and require specialized formulas and techniques. It also has limitations, as it can only be applied to objects that can be represented as a sphere or a portion of a sphere.

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