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Möbius strip

Möbius strip Shape or figure that can be modelled by giving a strip of paper a half-twist, then joining the ends together. It is of great interest in topology, being a one-sided surface (a line can be drawn along the strip of paper that will cover both sides, returning to the starting-point to meet itself). It was invented by August Ferdinand Möbius (1790–1868).

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Möbius strip

Mö·bi·us strip / ˈmōbēəs/ • n. a surface with one continuous side formed by joining the ends of a rectangular strip after twisting one end through 180°. Mobius strip.eps"/>

Möbius strip

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Möbius strip

Möbius strip

Resources

A Möbius strip is a twisted surface in space that is made by starting with a strip of paper, twisting one end through 180°, then joining it to the opposite end. That is, using the rectangular strip of paper shown in Figure 1, AC is joined to DB so that the point A coincides with the point D and the point C coincides with the point B.

The result is a one-sided surface. That is, any point P on it can be joined to its opposite, Q (or to any other point) by a path that does not cross the edge of the surface. This can be verified by running a finger or pencil along the Möbius strip, which is named after the nineteenth century mathematician, August Möbius.

If a Möbius strip is cut lengthwise along the center (inserting the scissors directly into the middle of the strip, not cutting in from the edge), the result will be a single two-sided loop with two twists. Re-cutting this loop produces two interlocking twisted loops (neither of them a Möbius strip).

If a original Möbius strip is cut lengthwise about a third of the way in from the edge, two interlocking loops are produced, one of them a Möbius strip and the other a two-sided loop.

The Möbius strip geometry is used in some conveyor belt systems (the idea being to extend belt life by distributing wear over both sides of the belt). It is mostly useful as a teaching tool in topology, the mathematical study of the properties of shapes and surfaces.

Resources

BOOKS

Pickover, Clifford A. The Mobius Strip: Dr. August Mobiuss Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology. New York: Thunders Mouth Pres, 2006.

Roy Dubisch

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Möbius Strip

Möbius strip

A Möbius strip is a twisted surface in space that is made by starting with a rectangular piece of paper , twisting one side through 180° (relative to the opposite side), and then joining it to the opposite side. That is, using the rectangle shown in Figure 1, AC is joined to DB so that the point A coincides with the point D and the point C coincides with the point B.

It is a one-sided surface. That is, any point P on it can be joined to its opposite, Q (or to any other point) by a path that does not cross the edge of the surface. It is named after the nineteenth century mathematician, August Möbius.

If a Möbius strip is cut length-wise the result will be just one two sided surface. If cut again, the result will be two interconnected surfaces that, again, are two sided.


Resources

books

Courant, Richard, and Herbert Robbins. What Is Mathematics? Oxford: Oxford University Press, 1948.

Smith, Karl J. The Nature of Modern Mathematics. Belmont, CA: Wadsworth Publishing Company, 1973.


Roy Dubisch

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