Möbius strip
Möbius Band
A surface with only one side and only one boundary (as a ring of paper that has been cut, one part turned 180 degrees, and reassembled), making it unorientable.
Origin
Discovered independently by German mathematicians Johann Benedict Listing and August Ferdinand Möbius in 1858, with precedence by publication date or first discovery going to Listing. Möbius encountered the strip while serving as chair of astronomy and higher mechanics at the University of Leipzig, working on the geometric theory of polyhedra. The Möbius strip is a non-orientable surface—one cannot consistently distinguish clockwise from counterclockwise within it. The discovery became fundamental to mathematical topology, the study of geometric properties that remain unchanged as objects are deformed.