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. | ||
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=31555
Möbius strip. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=M%C3%B6bius_strip&oldid=31555
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article