A Möbius strip is a surface with one and only one side. You might have seen a ring which has two distinct sides, one outside and one inside, but, as you see, the inside merges into the outside and the outside into inside in a Möbius strip. A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a single strip. The strip was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.
The Möbius strip is a peculiar object and has curious properties like:
(i) A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip of paper. This single continuous curve demonstrates that the Möbius strip has only one bound
ary.
(ii) If the strip is cut along the above line, instead of getting two separate strips, it becomes one long strip with two full twists in it, which is not a Möbius strip. This happens because the original strip only has one edge which is twice as long as the original strip of paper. Cutting creates a second independent edge, half of which was on each side of the knife or scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other.
The branch of Mathematics dealing with such objects is called Topology. Another such mysterious object is the Klein bottle, depicted on the left. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. The Klein bottle has no distinct outside or inside and has no edges.
The Möbius strip is a peculiar object and has curious properties like:
(i) A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip of paper. This single continuous curve demonstrates that the Möbius strip has only one bound
ary.(ii) If the strip is cut along the above line, instead of getting two separate strips, it becomes one long strip with two full twists in it, which is not a Möbius strip. This happens because the original strip only has one edge which is twice as long as the original strip of paper. Cutting creates a second independent edge, half of which was on each side of the knife or scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other.
The branch of Mathematics dealing with such objects is called Topology. Another such mysterious object is the Klein bottle, depicted on the left. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. The Klein bottle has no distinct outside or inside and has no edges.
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