I just have a question to a proof found here: https://nrich.maths.org/1384
At one point it says:
As eight copies of $\triangle$ will fill the sphere without overlapping.
Why this? Why can I "split" up a sphere into 8 identically triangles, of which any angle is $90°$ (so the angle-sum of a triangle is 270°) ?
Later it says
the total angle sum is $2\pi V$
(V... vertices). Why so?
The three coordinate planes cut the sphere into eight triangles $\Delta$.
The sum of the angles at each vertex of the triangulation is $2\pi$.
I think this was not terribly difficult $\ldots$