Navigating our obsession with one-sided objects. Möbius strips still fascinate mathematicians.

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A Mobius strip.
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▼ You have most likely encountered one-sided objects hundreds of times in your daily life—like the universal symbolfor recycling, found printed on the backs of aluminum cans and plastic bottles.
This mathematical objectis called a Möbius strip. It has fascinated environmentalists, artists, engineers, mathematicians, and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on September 26, 1868.
Möbiusdiscovered 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.
A Möbius strip can be created by taking a strip of paper, giving it an odd number of half-twists, then taping the ends back together to form a loop. If you take a pencil and draw a line along the center of the strip, you’ll see that the line apparently runs along both sides of the loop.
The concept of a one-sided object inspired artists like Dutch graphic designer M.C. Escher, whose woodcut “ Möbius Strip II” shows red ants crawling one after another along a Möbius strip.
The Möbius strip has more than just one surprising property. For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew. You may be astonished to find that you are left not with two smaller one-sided Möbius strips, but instead with one long two-sided loop. If you don’t have a piece of paper on hand, Escher’s woodcut “ Möbius Strip I” shows what happens when a Möbius strip is cut along its center line.
While the strip certainly has visual appeal, its greatest impact has been in mathematics, where it helped to spur on the development of an entire field called topology.
A topologist studies properties of objects that are preserved when moved, bent, stretched or twisted, without cutting or gluing parts together. For example,  (▪ ▪ ▪)

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