# Do Mobius Strips have a front and back?

Mobius strips, are generally held to have only one side - if one marks a place on the strip and on what looks like the other side then a pencil can draw a line between these two points without ever leaving the surface of the strip.

Technically this property is called non-orientability; and what we've done in the above demonstration is show that both 'sides' are path-connected.

So our intuition is shown to be limited and a little foolish.

However, one can as why then does it look as though it has two sides; a little thought shows that it is because we examine locally; in the same way that the earth looks flat, but in fact is round, and we resolve this tension by saying that the earth is locally flat; similarly we can say that the mobius strip is locally two-sided but not so globally.

(Now if the default adjective applied to the concept is local rather than global we could just simply say that the mobius strip is two-sided).

So, can we say that the Mobius strip has a front and back, despite all the write-ups it has had, by adding 'locally' as a qualifier?

• As you know, every manifold is locally orientable since each is locally homeomorphic to R^n. So any point on any surface is contained in a neighborhood with a front and back. Oct 29, 2014 at 4:53
• It was your answer to the question why objects have a front & back that inspired this question ;) Oct 29, 2014 at 5:20
• I agree completely with the reasoning in the question. Mobius strips do not have a global front and back but have a local front and back. Oct 29, 2014 at 20:57