Möbius strip
Möbius strip, geometric surface with one side and one boundary. First described in 1858, it is formed by giving a half-twist to a rectangular strip and joining the ends. Its properties have found applications in mathematics, engineering, physics, and art. See also Klein bottle.
The Möbius strip was independently discovered in 1858 by two German mathematicians, August Ferdinand Möbius and Johann Benedict Listing. They encountered the structure in their study of spatial properties and surfaces. However, the shape was known long before the 19th century, with shapes like the Möbius strip appearing in Roman art.
- Take a rectangular strip of paper.
- Give one end a half-twist (180 degrees).
- Join the ends together to form a loop.
The Möbius strip has several interesting properties. It is a nonorientable surface; that is, if an object travels around the strip, when it returns to its starting point, it will be inverted into its mirror image. The Möbius strip has only one edge; if an object moves along the edge, it will eventually return to its starting point without encountering a break. Cutting the strip along its center line will not produce two loops but a large loop with two twists. However, cutting the strip one-third of the way along its width would result in two linked loops, one of which is twice as long as the other.