Möbiusband

A Möbius band, also known as a Möbius strip or loop, is a surface that can be made by taking a strip of paper, cutting it, and then giving it a half-twist before joining the ends. This simple manipulation results in a surface with only one side and only one boundary.

Imagine you start drawing a line along the surface of a regular loop of paper. You would eventually return to your starting point without ever crossing an edge. Now, try the same on a Möbius band. You can trace a line that covers the entire surface and returns to its origin, effectively traversing what would be considered both "sides" of a normal loop. This property makes it a fascinating object in topology.

The discovery of the Möbius band is generally attributed to the German mathematicians August Ferdinand Möbius and Johann Benedict Listing, who independently described it in 1858. It has since become a popular example in mathematics, illustrating concepts like non-orientability and has found applications in art, design, and even engineering, such as in continuous conveyor belts or in the design of some resistors.