![]() It is not just a circular action it’s dynamic. There’s a depth to the image that reminds you to reduce, reuse and recycle. The green, three-arrowed universal sign for recycling also composes the Möbius band. Paintings have displayed Möbius shapes, as have earrings, necklaces and other pieces of jewelry. ![]() The Möbius strip has also been tailored to various artistic and cultural products. Conveyor belts use Möbius strips because they allow the entire surface area of the belt to receive an equal amount of wear, which makes it last longer. In the 1960s, Sandia Laboratories also used Möbius bands in the design of adaptable electronic resistors. For instance, Möbius strips are used in continuous-loop recording tapes, typewriter ribbons and computer print cartridges. Because it has never been observed in our organic environment, it is sometimes referred to as an “impossible shape.” Practical applications of it abound in the world of human invention, however. But the strip was long thought never to occur in the natural world. You can make a model of the Möbius strip with just a rectangular piece of paper: give it an odd number of half-twists, then tape the ends back together. 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. 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. August Ferdinand Möbius was a mathematician and theoretical astronomer (and also the first to introduce “homogenous coordinates” into “projective geometry”). The Möbius strip was independently discovered by two German mathematicians in 1858. 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.’” The unorientable quality of the Möbius strip is perhaps its most distinctive. ‘Time passes.’ ‘That’s how it goes,’ Aureliano admitted, ‘but not so much.’” An exchange between two family members illustrates this central theme: “Úrsula sighed. Melding history, memory, and prophecy, the novel follows the Buendía family through cyclical patterns of behavior and emotion. One salient literary example is Gabriel García Márquez’s One Hundred Years of Solitude. ![]() Artists and authors explore this phenomenon as well. The continuum of crossing a Möbius strip is emblematic of how we experience time in a nonlinear way. We might ask ourselves after 2020, where are we? Have we spun around after so much chaos, and found our position stagnated, back where we started? Or are we at a new beginning? ![]() The figurative and narrative implications of the Möbius strip are rich: when you try to go forward, you ring sideways, when you try to circle in, you find yourself outside. After two loops, the ant would be back at the beginning-but dizzy. ![]() One apparent loop would land the ant not where it started but upside down, only halfway through a full circuit. Picture the insect traversing the Möbius band. A typical thought experiment to demonstrate how the three-dimensional strip operates involves imagining an ant on an adventure. A single-sided surface with no boundaries, the strip is an artist’s reverie and a mathematician’s feat. If you were to trace both “sides” of a Möbius strip, you would never have to lift your finger. ![]()
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