Tuesday, January 23, 2018

[weallkmp] Constant curvature

Curved manifolds become interesting in at least 2 dimensions.  (Are there any interesting things to do on a 1-dimensional curved manifold?  Maybe serve as a baseline for text.)

Constant curvature is the simplest type of curvature.  A 2D manifold with constant positive curvature is the surface of a sphere.  Constant negative curvature is (I think) hyperbolic space, for example Escher's Circle Limit series.  Also pseudosphere.

Create software tools for working in these spaces, for example for a game: how to address a point, compute distances and angles.

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