"This enigmatic shape is incredibly easy to make: Take a long strip of paper and bring both ends together. But before you glue the ends to each other, rotate one by 180 degrees. The result is a twisted band. From a mathematical perspective, Mobius strips are fascinating because they have only one surface and one edge. Unlike a cylindrical object (such as one created by gluing together the ends of a strip that hasn't been twisted), there is no inside or outside."
"For physicists, these twisted shapes make for excellent points of comparison when contemplating the properties of subatomic particles, such as the spin of the electron, which must be rotated by 720 degrees to get back to its start. And in factories, Mobius strips have been used as conveyor belts because they wear out significantly more slowly than untwisted belts, for which only one side is stressed."
Klein bottle origins connect to the Mobius strip, a twisted paper band formed by joining ends after a 180-degree rotation. The Mobius strip has only one surface and one edge, so there is no distinct inside or outside. Physicists use nonorientable shapes as analogies for particle properties like electron spin, which requires a 720-degree rotation to return to its original state. Industries have used Mobius-configured conveyor belts because they distribute wear across both sides and last longer. The surface permits continuous traversal without lifting a finger. Felix Klein investigated further constructions by gluing strips together along edges.
Read at www.scientificamerican.com
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