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.
No comments :
Post a Comment