Certain highly-symmetric spaces whose points represent lines in the plane have the shape of a Möbius strip. A Möbius strip without its boundary, called an open Möbius strip, can form surfaces of constant curvature.

Both the Sudanese Möbius strip and another self-intersecting Möbius strip, the cross-cap, have a circular boundary. The Sudanese Möbius strip is a minimal surface in a hypersphere, and the Meeks Möbius strip is a self-intersecting minimal surface in ordinary Euclidean space. A thin paper strip with its ends joined to form a Möbius strip can bend smoothly as a developable surface or be folded flat the flattened Möbius strips include the trihexaflexagon. 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

Mobius coil null vector waves