# Moebius Strip

The Möbius Strip (also Moebius) is a surface with only one side and one edge. It can be made by putting a half-twist in a piece of paper and gluing the ends together.

Mathematically, it can be parametrised by:

$x = \cos u + v\cos\frac{nu}{2}\cos u$
$y = \sin u + v\cos\frac{nu}{2}\sin u$
$z = v\sin\frac{nu}{2}$,

where n is the number of half-twists, u runs from 0 to 4π and v from 0 to 0.3 (this can be varied to alter the width). n=1 gives the standard Möbius Strip, while any integer gives a continous strip with n half twists in it. If n is not an integer, the surface may be discontinuous (depending on how far u runs).

## Non-integer nEdit

By setting n to non-integer values between 0 and 1, we can see a flat band "unwrap" into a Möbius strip: