Möbius strip
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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