Möbius Born, His Strip Soon Discovered

Möbius Born, His Strip Soon Discovered

“On this day in 1790, the German mathematician August Ferdinand Möbius was born in Schulpforta, not far from Leipzig. His name is attached to a variety of important mathematical, topographical and astronomical discoveries, the best known of which is the Möbius strip.

Möbius showed an early inclination towards mathematics and despite family wishes that he pursue law, he followed his interests, studying mathematics, astronomy, and physics. After studies at the University of Leipzig, Möbius went on to study at the University of Göttingen under one of the greatest mathematicians in history, Carl Friedrich Gauss.

In 1858, Möbius and another German mathematician, Johann Benedict Listing, both independently discovered the properties found in what is now known as the Möbius strip (or band), which is essentially a two-dimensional surface with only one side, best described as a band with a 180-degree twist. It can be created by taking a strip of paper–resembling an elongated rectangle–and bringing the ends together to form a loop. One end is then given a one-half twist (180 degrees) before fastening it to the other end.

The result, as found in M.C. Escher’s famous picture of ants marching endlessly around a strip, has fascinated school children and mathematicians alike for centuries. The band, as illustrated by Escher, has only one side and so if an ant were to walk along the strip it would seemingly end up on the opposite side at the end of an attempted complete rotation.

Möbius strips have a number of useful applications. They have been used in machinery as conveyor belts since they last longer, recording tapes since they double the playing time, in printer and typewriter ribbons, and are even a symbol for recycling.

Aside from the strip, Möbius’s name is also attached to other mathematical discoveries, including the Möbius function and the Möbius inversion formula, both considered important contributions to number theory. Möbius excelled in the field of astronomy as well, and served as a professor of astronomy at the University of Leipzig and the director of the city’s observatory. There is a crater named after him on the far side of the Moon.”

Credit: Getty 95444653
Caption: A Möbius strip can be created by taking a strip of paper and bringing the ends together to form a loop.