12 Dec
2000
12 Dec
'00
12:08 p.m.
On Mon, 11 Dec 2000, R. A. Hettinga wrote:
Chambers defines geodesic as "the shortest line on a surface between two points on it"
Thank you. It works in all dimensions, and, thus it's topological, right?
Topology does not deal with dimension or distance. Pure geometry. Not even affine or anything. As I've seen them defined, geodesics do not necessarily mean the shortest path but rather the shortest path based on local knowledge. I.e. if you have a wormhole in general relativity, the possible shortcut does not affect the definition of geodesics in any way. You calculate the geodesic based on the local curvature measure of the space, that's it. Sampo Syreeni <decoy@iki.fi>, aka decoy, student/math/Helsinki university