![]() ![]() It can be swept as a ruled surface by a line segment rotating in a rotating plane, with or without self-crossings. ![]() Several geometric constructions of the Möbius strip provide it with additional structure. All of these embeddings have only one side, but when embedded in other spaces, the Möbius strip may have two sides. Any two embeddings with the same knot for the centerline and the same number and direction of twists are topologically equivalent. Every non-orientable surface contains a Möbius strip.Īs an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a knotted centerline. ![]() The Möbius strip is a non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. 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. 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. A Möbius strip made with paper and adhesive tape ![]()
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