M.C. Escher was an amazing surrealist artist whose works were frequently inspired by mathematics. Here is his 1963 work, “Moebius Strip II,” which shows ants crawling along the single-surface loop.
First discovered by astronomer and mathematician August Möbius in 1858 (although it had been described in unpublished literature a few years prior by a different researcher), the Möbius strip inspired the whole mathematical field of topology, which studies the properties of surfaces. Topologically similar surfaces are the same if they can be stretched or bent to look alike without being cut or glued together.
Topologically similar objects also have another property in common, called “orientability,” which is where the Möbius strip comes in. If an object has a consistent clockwise or counterclockwise orientation, it is orientable. And the Möbius strip, unlike a two-sided loop, is not.
This matters IRL. For instance, molecular compounds that are not similarly oriented have very different properties when they are facing different directions. So even though the Möbius strip might look just like a parlor trick or a trippy painting, this 19th-century German’s work is studied today with practical applications.
Sources: “The Mathematical Genius of Möbius Strips and Other One-Sided Objects”, David and Richard Gunderman, Smithsonian Magazine, Sept 25 2018
