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Mobius strip discovered
You have most likely encountered one-sided objects hundreds of times in your daily life — like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles. This mathematical object is called a Mobius strip. Another mathematician named Listing actually described it a few months earlier, but did not publish his work until The concept of a one-sided object inspired artists like Dutch graphic designer M. For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew. 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.
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Möbius Strip -- from Wolfram MathWorld
Like the cylinder , it is not a true surface, but rather a surface with boundary Henle , p. According to Madachy , the B. Trott, pers. The coefficients of the first fundamental form for this surface are.
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Möbius Strip and Its Inventor
It can be realized as a ruled surface. Its boundary is a simple closed curve, that is, homeomorphic to a circle. Some of these can be smoothly modeled in Euclidean space , and others cannot.