Afghan Bands or The Perplexing Mystery of the Moebius Bands, is a self-working topological magic effect where long loops of paper are cut lengthwise to produce two separate loops as expected, then as two interlocked loops, and finally as a single double-length loop.
It is based on the mathematical Möbius Strip which was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. It became a popular magic trick in the late 1800s after being published in Popular Scientific Recreations by Gaston Tissandier, which was the English translation of his Les récréations scientifiques (1881).
Perhaps the first professional magic act to include the effect was by Félicien Trewey who was performing it by the late 1800s. Ellis Stanyon was marketing a commercial version by 1900 as "Mystic Afgan [sic] Bands" in Britain. In the 1920s James C. Wobensmith came up with the now standard twists and marketed it as "The Red Muslin Bands." He also substituted muslin cloth which made the effect faster because they could be hand torn rather than slowly cut with scissors. In 1977 Ed Eckl marketed as "Möby-Zip" which used zippered cloth.