# Continuous Unit Normal Field.

1. Aug 20, 2011

### JG89

So I've been reading about orientated surfaces lately, and I always see the definition that a surface S is orientable if it is possible to choose a unit normal vector n, at every point of the surface so that n varies continuously over S.

However, what does "varies continuously" mean? I never see this statement made precise and it is ambiguous (to me at least)

2. Aug 20, 2011

### Hurkyl

Staff Emeritus
It means if you write n as a function of P (the point on the surface to which n is normal), that function is continuous.

3. Aug 21, 2011

### JG89

So let's take the Mobius Strip. If p is any point on the strip and n is a unit normal to p, and we transverse the strip and come back to the same point p, then we end up with the unit normal -n, where we should have had it as n, since the unit normal should have been continuous, right? And this is our contradiction?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook