Moebius Strip
From Wikimedia Commons, the free media repository
The Möbius Strip (also Moebius) is a surface with only one side and one edge. It can be made by putting a halftwist in a piece of paper and gluing the ends together.
Mathematically, it can be parametrised by:
 ,
where n is the number of halftwists, 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).
Basic Möbius Strip (n=1)[edit]
Noninteger n[edit]
By setting n to noninteger values between 0 and 1, we can see a flat band "unwrap" into a Möbius strip:

Moebius Surface 01.gif
Animated Version