M¶bius strip From Wikipedia, the free encyclopedia. A M¶bius strip made with a piece of paper and tape. The M¶bius strip or M¶bius band is a topological object with only one side (one-sided surface ) and only one boundary component . It was co-discovered independently by the German mathematicians August Ferdinand M¶bius and Johann Benedict Listing in . A model can easily be created by taking a paper strip and giving it a half-twist, and then merging the ends of the strip together to form a single strip. In Euclidean space there are in fact two types of M¶bius strips depending on the direction of the half-twist: clockwise and counterclockwise . The M¶bius strip is therefore chiral , which is to say that it is "handed". The M¶bius strip has several curious properties. If you try to split the strip in half by cutting it down in middle along a line parallel to it's edge, instead of getting two separate strips, it becomes one long strip with two half-twists in it (not a M¶bius strip). If you cut this one down the middle, you get two strips wound around each other. Alternatively, if you cut along a M¶bius strip, about a third of the way in from the edge, you will get two strips; one is a thinner M¶bius strip, the other is a long strip with two half-twists in it (not a M¶bius strip). Other interesting combinations of strips can be obtained by making M¶bius strips with two or more flips in them instead of one. For example, a strip with three half-twists, when divided lengthwise, becomes a strip tied in a | |
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