Tagged Questions
0
votes
0answers
115 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
120 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
1answer
218 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
144 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 ...
2
votes
1answer
289 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
361 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 + ( ...
5
votes
2answers
2k 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 ...
