0
votes
0answers
29 views

Find the angles defining an hyperspherical cap

For the hyperspherical cap of dimension $n+1$ find all the angle $\phi_1, \phi_2, \ldots, \phi_n$ which defines the cap? I mean, I know a cap is usually define by its height $h$ and its base $a$. ...
1
vote
0answers
346 views

Generating evenly distributed points on a sphere

How could I write an algorithm to generate n points distributed 'evenly' on a sphere? I already wrote an algorithm to generate points distributed uniformly on the surface (here), but by 'evenly' ...
4
votes
1answer
178 views

Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
5
votes
2answers
289 views

Elementary arguments concerning the stereographic projection

How does one give a proof that is short; and strictly within the bounds of secondary-school geometry that the stereographic projection is conformal; and maps circles to circles?
2
votes
0answers
194 views

Is there a similar formula in spherical and hyperbolic geometry as Euclidean Geometry?

In an Euclidean plane, we know that the area of a triangle is determined by the length of base and the height, then is there a similar thing do happen in Spherical and hyperbolic spaces? In ...
3
votes
1answer
540 views

Arc length of a great circle which is the hypotenuse of an isoceles right triangle on the sphere

I am doing a problem which requires me to find the arclength of the hypotenuse of an isosceles right triangle. (The book calls it a 2 Dimensional Sphere but I hope that is a typo) I start at the ...
1
vote
1answer
705 views

Formula for the coordinate of the midpoint in spherical coordinate system

Please let me know the formula for the coordinate of the midpoint of 2 points in spherical coordinate system . If possible , I want the answer includes the exact formula as , midpoint = point1 + ( ...
6
votes
2answers
4k views

Proof that the angle sum of a triangle is always greater than 180 degrees in elliptic geometry

I've scoured the internet and have found many proofs showing that in Euclidean geometry, the angle sum of a triangle is always 180 degrees. I've also found many proofs showing that in hyperbolic ...