If we lived in a nonorientable world, these chemicals would be indistinguishable.Īugust Möbius’s discovery opened up new ways to study the natural world. Its mirror image, D-methamphetamine, is a Class A illegal drug. For example, the chemical L-methamphetamine is an ingredient in Vicks Vapor Inhalers. These chemical compounds have the same chemical structures except for one key difference: They are mirror images of one another. The concept of orientability has important implications. This transformation is impossible on an orientable surface like the two-sided loop. Somehow, the configuration has morphed into its own mirror image, but all we’ve done is move it around on the surface. However, we can move the three-dot configuration around the Möbius strip such that the figure is in the same location, but the colors of the dots listed off clockwise are now red, blue and black. When the GIF starts, the dots listed off clockwise are black, blue and red. Since the Möbius strip is nonorientable, whereas the two-sided loop is orientable, that means that the Möbius strip and the two-sided loop are topologically different. On the two-sided loop, the note will always read from left to right, no matter where your journey took you. On a nonorientable surface, you may come back from your walk only to find that the words you wrote have apparently turned into their mirror image and can be read only from right to left. The surface is orientable if, when you come back from your walk, you can always read the note. Imagine writing yourself a note on a see-through surface, then taking a walk around on that surface. Like its number of holes, an object’s orientability can only be changed through cutting or gluing. Instead, the property that distinguishes a Möbius strip from a two-sided loop is called orientability. Unfortunately, a Möbius strip and a two-sided loop, like a typical silicone awareness wristband, both seem to have one hole, so this property is insufficient to tell them apart – at least from a topologist’s point of view. This property – called the “genus” of an object – allows us to say that a pair of earbuds and a doughnut are topologically different, since a doughnut has one hole, whereas a pair of earbuds has no holes. The number of holes in an object is a property which can be changed only through cutting or gluing. Because both objects have just one hole, one can be deformed into the other through just stretching and bending. No cutting or gluing is required to transform between them.Īnother pair of objects that are topologically the same are a coffee cup and a doughnut. For example, a tangled pair of earbuds is in a topological sense the same as an untangled pair of earbuds, because changing one into the other requires only moving, bending and twisting. 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.Ī topologist studies properties of objects that are preserved when moved, bent, stretched or twisted, without cutting or gluing parts together. 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. 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. For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew. The Möbius strip has more than just one surprising property. Escher, whose woodcut “ Möbius Strip II” shows red ants crawling one after another along a Möbius strip. The concept of a one-sided object inspired artists like Dutch graphic designer M.C. 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. 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.
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