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In a non-Euclidean space with sufficient negative (hyperbolic) curvature it should indeed be possible to have a convex octagon with four 90° internal angles. Ju
by Sharlin 6y ago
In a non-Euclidean space with sufficient negative (hyperbolic) curvature it should indeed be possible to have a convex octagon with four 90° internal angles. Just like in a space with positive curvature, such as the surface of a sphere, it is possible for a triangle to have three 90° internal angles.
- sandworm101 6y agoIf you are willing to start stretching space then we can throw all the polygon definitions out the window. With a strong enough curve in space a sphere can start having corners.
- firethief 6y agoThat can get arbitrarily close to true, but I think it is false
- redvenom 6y agoNo, polygons in non-Euclidean space makes sense. Polygons and more generally, geometric simplicial complexes in other spaces is a branch of mathematics all by itself (geometric group theory), so you certainly shouldn't "throw it out the window".
- BlueTemplar 6y agoCan it ?