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# Is it true that the Möbius strip﻿ is not impossible?

Question #115507. Asked by SiegeTank55. (Jun 24 10 9:39 PM)

Zbeckabee

Not impossible...in what regard?

A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having traversed every part of the strip without ever crossing an edge.

The Möbius strip has several curious properties. 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. This single continuous curve demonstrates that the Möbius strip has only one boundary.

Cutting a Möbius strip along the center line yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip. This happens because the original strip only has one edge which is twice as long as the original strip. Cutting creates a second independent edge, half of which was on each side of the scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists.

If the strip is cut along about a third of the way in from the edge, it creates two strips: One is a thinner Möbius strip — it is the center third of the original strip, comprising 1/3 of the width and the same length as the original strip. The other is a longer but thin strip with two full twists in it — this is a neighborhood of the edge of the original strip, and it comprises 1/3 of the width and twice the length of the original strip.

http://en.wikipedia.org/wiki/M%C3%B6bius_strip

 Jun 24 10, 10:44 PM
looney_tunes

To make one and see for yourself, take a strip of paper and bend it to make a circle. Before taping the ends together, twist one end halfway around (so the edge that was on the bottom is now on the top). When you tape the ends together, you will have a mobius strip.

 Jun 24 10, 11:36 PM

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