In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE. The Möbius strip is a non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip.
A Möbius strip made with paper and adhesive tape
Mosaic from ancient Sentinum depicting Aion holding a Möbius strip
Chain pump with a Möbius drive chain, by Ismail al-Jazari (1206)
Endless Twist, Max Bill, 1956, from the Middelheim Open Air Sculpture Museum
August Ferdinand Möbius was a German mathematician and theoretical astronomer.
August Ferdinand Möbius
1843 copy of Die Elemente der Mechanik des Himmels
First page to a 1843 copy of Die Elemente der Mechanik des Himmels