I am currently researching a book about applying the Möbius Strip to magic. Mathematicians use this principle to understand topology and inventors have patented contraptions that use the Möbius Strip. The one-sided band has also inspired sculptors and composers, as shown in my Pinterest collection below. Clifford A. Pickover has written a fascinating book about the Möbius Strip in mathematics, games, literature, art, technology, and cosmology.
The Afghan Bands
Magicians know this trick as the Afghan Bands. This name stems from a time when the Western world associated Afghanistan with magic and mysticism, instead of with war and terrorism.
The Afghan Bands is one of the few magic tricks that is purely based on topology. Many tricks have a topological theme, such as the Gozinta Boxes, but their method is not topology.
The magic literature has many references to this trick. Some magicians have developed techniques to increase the deceptiveness of this routine. Most literature consists of suggestions on how to present this trick entertainingly.
The Afghan Bands were trendy until the 1950s. Studying the history of this basic trick unravels an intricate web of magical innovation and accusations of plagiarism. The history of the Afghan Bands teaches us about how magicians innovate and develop technical principles into pieces of theatrical magic.
There are several commercial version of the Afghan Bands. Most innovations in this trick relate to replacing the paper with muslin so that the bands can be ripped instead of cut. Harry Blackstone popularised this version which he called the Red Rags. In the 1980s the Afghan Zipper or Möby Zip appeared on the market. In this version, a zipper separates the bands into two to speed-up the process.
This book is in production and will be available in December 2017.
Afghan Bands and Möbius Strip Videos
The videos below show the Möbius Strip as a magic trick and some theoretical aspects of this principle.