# Difference between revisions of "Möbius strip"

From Encyclopedia of Mathematics

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− | A non-orientable surface with [[Euler characteristic|Euler characteristic]] zero whose boundary is a closed curve. The Möbius strip can be obtained by identifying two opposite sides | + | {{TEX|done}} |

+ | A non-orientable surface with [[Euler characteristic|Euler characteristic]] zero whose boundary is a closed curve. The Möbius strip can be obtained by identifying two opposite sides $AB$ and $CD$ of a rectangle $ABCD$ so that the points $A$ and $B$ are matched with the points $C$ and $D$, respectively (see Fig.). | ||

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/m064310a.gif" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/m064310a.gif" /> | ||

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Figure: m064310a | Figure: m064310a | ||

− | In the Euclidean space | + | In the Euclidean space $E^3$ the Möbius strip is a one-sided surface (see [[One-sided and two-sided surfaces|One-sided and two-sided surfaces]]). |

The Möbius strip was considered (in 1858–1865) independently by A. Möbius and I. Listing. | The Möbius strip was considered (in 1858–1865) independently by A. Möbius and I. Listing. |

## Latest revision as of 20:10, 11 April 2014

A non-orientable surface with Euler characteristic zero whose boundary is a closed curve. The Möbius strip can be obtained by identifying two opposite sides $AB$ and $CD$ of a rectangle $ABCD$ so that the points $A$ and $B$ are matched with the points $C$ and $D$, respectively (see Fig.).

Figure: m064310a

In the Euclidean space $E^3$ the Möbius strip is a one-sided surface (see One-sided and two-sided surfaces).

The Möbius strip was considered (in 1858–1865) independently by A. Möbius and I. Listing.

**How to Cite This Entry:**

Möbius strip.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=M%C3%B6bius_strip&oldid=23422

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article