- #1
FallenApple
- 566
- 61
So if I pick any 2 points on a 2d manifold, say x1 and x2, then the distance between these two points is a secant line that passes through 3 space that isn't part of the manifold. So no matter what, there doesn't exist an point epsilon, e , where ||e ||>||0 || and ||x2-x1||<|| e ||
No matter how small we shrink the neighborhood by decreasing the length of e, the distance, ||x2-x1|| is the distance of a secant line that does not lie on the curved surface itself. So it seems that there is no neighborhood on a surface that is euclidian.
No matter how small we shrink the neighborhood by decreasing the length of e, the distance, ||x2-x1|| is the distance of a secant line that does not lie on the curved surface itself. So it seems that there is no neighborhood on a surface that is euclidian.