- #1
maze
- 662
- 4
Are there surfaces that have a geodesic curve which completely covers the surface, or (if that's not possible) is dense in the surface?
In other words, if you were standing on the surface and started walking in a straight line, eventually you would walk over (or arbitrarily close to) every point on the surface.
My current thinking is of a torus where you start walking at a wonky angle so that your path never repeats, like so, but I'm not sure if it quite works:
http://img517.imageshack.us/img517/4487/torusgeodesicap9.png
In other words, if you were standing on the surface and started walking in a straight line, eventually you would walk over (or arbitrarily close to) every point on the surface.
My current thinking is of a torus where you start walking at a wonky angle so that your path never repeats, like so, but I'm not sure if it quite works:
http://img517.imageshack.us/img517/4487/torusgeodesicap9.png
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