"This curious surface is called a Möbius
Strip or Möbius Band, named after August Ferdinand Möbius,
a nineteenth century German mathematician and astronomer, who was a
pioneer in the field of topology. Möbius, along with his better
known contemporaries, Riemann, Lobachevsky and Bolyai, created a non-Euclidean
revolution in geometry.
Möbius strips have found a number of surprising
applications that exploit a remarkable property they possess: one-sidedness.
Joining A to C and B to D (no half twist) would produce a simple belt-shaped
loop with two sides and two edges -- impossible to travel from one side
to the other without crossing an edge. But, as a result of the half
twist, the Möbius Strip has only one side and one edge!"