How to do a Moebius strip.

1. Start with a long rectangle (ABCD) made of paper.

2. Give the rectangle a half twist.

3. Join the end so that A is matched with D and B is matched with C.

This 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!**

Giant Möbius Strips have been used as conveyor belts (to make them last longer, since “each side” gets the same amount of wear) and as continuous-loop recording tapes (to double the playing time). In the 1960’s Sandia Laboratories used Möbius Strips in the design of versatile electronic resistors. Free-style skiers have christened one of their acrobatic stunts the Möbius Flip.

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