- 561

- 60

**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.