Introduction

The Möbius strip is named after mathematician and astronomer August Ferdinand Möbius. He came up with the idea in September 1858. German mathematician Johann Benedict Listing independently thought of the same idea in July 1858. Unfortunately for Listing, one of the most famous surfaces in mathematics was named for Möbius, not Listing.

What is the Mobius strip?

So what’s the big deal with the Möbius strip? It’s quite simple, actually. The Mobius strip is famous because it has only one side and one edge. Möbius strip, a one-sided surface that can be constructed by affixing the ends of a rectangular strip after first having given one of the ends a one-half twist. This space exhibits interesting properties, such as having only one side and remaining in one piece when split down the middle. If you were to trace both “sides” of a Möbius strip, you would never have to lift your finger.

A single-sided surface with no boundaries, the strip is an artist’s reverie and a mathematician’s feat. A typical thought experiment to demonstrate how the three-dimensional strip operates involves imagining an ant on an adventure. Picture the insect traversing the Möbius band. One apparent loop would land the ant not where it
started but upside down, only halfway through a full circuit. After two loops, the ant would be back at the beginning—but dizzy. The unorientable quality of the Möbius strip is perhaps its most distinctive. Orientability can be defined as “a continuous choice of
local orientation.” A more colloquial explanation: “a space is orientable if you can choose ‘inward’ and ‘outward’ or ‘up’ and ‘down’ directions at every point on the surface that are compatible: you will never accidentally end up at the same point but with ‘up’ flipped to ‘down.’”

Discovery

The Möbius strip was independently discovered by two German mathematicians in 1858. August Ferdinand Möbius was a mathematician and theoretical astronomer (and also the first to introduce “homogenous coordinates” into “projective geometry”).

Johann Benedict Listing, a younger mathematician, coined the term “topology” for the study of surfaces, and in conducting that research, independently determined the properties of the Möbius strip. Though perhaps too neat a metaphor, it’s interesting to note that these two men arrived at the same conclusion, from different directions, at the same time.Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician
named Listing actually described it a few months earlier, but did not publish his work until 1861.) Möbius seems to have encountered the Möbius strip while working on the geometric theory of polyhedra, solid figures composed of vertices, edges and flat faces.

The Scientists

August Ferdinand Möbius, (born November 17, 1790, Schulpforta, Saxony [Germany]—died September 26, 1868, Leipzig), German mathematician and theoretical
astronomer who is best known for his work in analytic geometry and in topology. In the latter field he is especially remembered as one of the discoverers of the Möbius strip.

Johann Benedict Listing, (born July 25,Frankfurt – died December 24,
1882,Göttingen.),German mathematician who coined the term "topology" for the study
of surfaces. During his inquiries into topology, Listing independently discovered the properties of the Möbius strip, established by August Möbius in 1865. Listing also
produced major works on the mathematical descriptions of optics and other works of applied (as opposed to "pure") mathematics.

Written by Joseph Oduyebo
Sources: https://www.britannica.com/science/Mobius-strip

https://wonderopolis.org/wonder/What-Is-a-M%C3%B6bius--Strip
https://www.scientificamerican.com/article/the-timeless-journey-of-the-moe
bius-strip/
https://www.smithsonianmag.com/science-nature/mathematical-madness-m
obius-strips-and-other-one-sided-objects-180970394/#:~:text=M%C3%B6bi
us%20discovered%20the%20one%2Dsided,publish%20his%20work%20until
%201861.)
https://www.britannica.com/biography/August-Ferdinand-Mobius
https://en.wikipedia.org/wiki/Johann_Benedict_Listing