Möbius strip

Also known as Moebius strip, Moebius band, Möbius band, Mobius strip, Mobius band

two-dimensional surface with only one side and only one edge

AI overview

A Möbius strip is a flat surface created by twisting a strip of paper and connecting its ends together, which results in a shape that has only one side and one edge instead of the two sides and edges you'd normally expect. It's a fascinating mathematical object that challenges our everyday intuition about how surfaces work and has inspired artists, engineers, and mathematicians for over 150 years.

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Image: Möbius strip.jpg

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Commons category: Moebius strip
time of discovery or invention: 1858-00-00
Commons gallery: Moebius Strip

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Article

A paper Möbius strip 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.

As 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. Any two embeddings with the same knot for the centerline and the same number and direction of twists are topologically equivalent. All of these embeddings have only one side, but when embedded in other spaces, the Möbius strip may have two sides. It has only a single boundary curve.