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
The ouroboros or uroboros is an ancient symbol depicting a serpent or dragon eating its own tail. The ouroboros entered Western tradition via ancient Egyptian iconography and the Greek magical tradition. It was adopted as a symbol in Gnosticism and Hermeticism and most notably in alchemy. Some snakes, such as rat snakes, have been known to consume themselves.
An ouroboros in a 1478 drawing in an alchemical tract
First known representation of the ouroboros, on one of the shrines enclosing the sarcophagus of Tutankhamun
A highly stylised ouroboros from The Book of Kells, an illuminated Gospel Book (c. 800 CE)
Engraving of a wyvern-type ouroboros by Lucas Jennis, in the 1625 alchemical tract De Lapide Philosophico. The figure serves as a symbol for mercury.