WGS-84 GANG. There's a wonderful little puzzle game called Anti-Chamber which is based on non-euclidean geometry. If you're a g*mer and haven't played it, I highly recommend it.
This reminds me of a very beautiful result in spherical geometry, called Girard’s Theorem:
On the unit sphere, a spherical triangle with angles A, B, and C has area A + B + C - π.
The standard proof involves looking at a diagram, and it’s extremely pleasant once you digest it all. I remember being very proud to recreate the diagram and get it all sorted out in my head.
Here’s a nice little intro on the topic: https://www.math.csi.cuny.edu/abhijit/623/spherical-triangle.pdf
I was relieved to be done with my math minor and now I'm avoiding studying for finals by reading lecture notes for a math class I'm not in.
Can someone smarter than me explain how much I should be afraid please?
OP thinks this is weird because in Euclidean geometry the sum of all internal angles in a triangle should add up to 180 degrees, but this is spherical geometry so the same rules don't apply.
Not all, its just non-euclidian geometry, nothing to worry about. The stuff you learn at school, about triangles, and geometry and shit, only applies when the planes are "striaght". When these planes are curved (like the surface of a sphere is) then some of these rules change - i.e. a triangles angles no longer add up to 180...
Joke's on you, I don't have the math knowledge to lose sanity points from this.
Obviously a proof that the earth cannot be a sphere. Its school maths to know that the angles of a triangle add up to 180. No sanity points lost. This post brought to you by flatcom gang.
I still don't follow. Isn't that exactly what you'd expect on a sphere? If you made the triangle even bigger, you could get the angles to add up to 540.
