A paperfolding paradise
The website of writer and paperfolding designer David Mitchell
|The Mobius Strip / The Afghan Bands / Les Anneaux Mysterieuse|
page attempts to record what is known about the origin
and history of the Mobius Strip and the magical effect
commonly known as the Afhghan Bands. Please contact me if
you know any of this information is incorrect or if you
have any other information that should be added. Thank
The Mobius Strip
When made of paper a Mobius Strip can be considered to be a folded object even though it does not contain any creases.
The earliest known image of a Mobius Strip is found in the central part of a mosaic from a Roman villa in Sentinum which can be dated to around 200250CE. This Mobius Strip is probably not a representation of an actual object. An untwisted band is found in other similar portrayals of this mythical scene. Information from 'Mobius strips before Mobius: Topological hints in ancient representations' by Julyan H. E. Cartwrigh and Diego L. Gonzalez available online at https://arxiv.org/pdf/1609.07779.pdf.
A pumping mechanism using Mobius Strip topology is found in the 'Book of Knowledge of Ingenious Mechanical Devices' written by Al-Jazari in 1206. Information from 'Mobius strips before Mobius: Topological hints in ancient representations' by Julyan H. E. Cartwrigh and Diego L. Gonzalez available online at https://arxiv.org/pdf/1609.07779.pdf.
In 1858 Johann Benedict Listing (1808 - 1882), a German mathematician, made notes containing a description of a Mobius Strip, which were not, however, published until 1861.
Also in 1858, but a few months later, another German mathematician, August Ferdinand Möbius, made a similar discovery. This was not published until 1865 (after his death).
Both men had studied under Carl Friedrich Gauss, the best German mathematician of the era, and it is possible that Gauss was the common factor in these discoveries. Information from 'History of the Möbius Band' https://sites.google.com/site/themobiusbandart/history-of-the-moebius-band.
I do not know if either of these discoveries involved papefolding.
The Setinum mosaic pictured above has been in the possession of the Glyptothek Museum in Munich since 1828. It is therefore possible that either Gauss, Listing or Mobius might have seen this early depiction of a Mobius Strip and have been influenced by it.
Volume 3 of Tom Tit's 'La Science Amusante', published by Editions Larousse in Paris in 1893. contains a section showing how to construct a Mobius Strip that can then be flattened to create a regular hexagon.
The Afghan Bands / Les Anneaux Mysterieuse
The Afghan Bands is a self-working magical effect in which three apparently identical long loops of paper (or sometimes cloth) are cut (or sometimes torn) lengthwise to produce first two separate loops, then a single double-length loop, and finally two interlocked loops. The first loop is a simple untwisted loop, the second a Mobius Strip and the third a fully twisted loop.
According to https://geniimagazine.com/wiki/index.php?title=Afghan_Bands 'The first professional magician to perform the effect was Felicien Trewey in the late 1800s' and 'Percy Selbit was the first to describe the Möbius strip as a method for a magic trick in the English language in 1901, coining the name 'Afghan Bands'.' I have not been able to verify this information.
The first publication of the effect that I know of is in 'Le Livre des Amusettes' by Toto, which was published in Paris by Charles Mendel in 1899.
The effect also appeared as 'An Episode of Mere Man' in Will Blyth's 'Paper Magic, first published in London in 1920 and as 'Trewey's Paper Rings' in 'Houdini's Paper Magic' first published in New York in 1922.
It also appeared in 'Fun with Paperfolding' by Murray and Rigney, published in New York in 1928, as 'The Mystery Loops'.