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Mobius strip

, 09:22, 1 August 2007
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Then the Mobius strip is the trace of a moving open line segment of length twice the half-width whose center traces the midcircle, and which rotates at a rate of half that at which it revolves.

There is also another, diffeomorphic, notion of Mobius strip which is very different in the sense of its metric. Check out [[flat Mobius strip]].
==Equational descriptions==
[itex](x,1) \sim (-x,-1), (1,y) \sim (-1,y)[/itex]
{{double cover|right circular cylinder}}

The Mobius strip has a double cover which is the right circular cylinder. However, the pull-back metric on this is not the same as the usual metric on the right circular cylinder.

==Structure and symmetry==

===Homeomorphisms===

Topologically, any two points on the Mobius strip are equivalent, viz there is a homeomorphism taking any point to any other point.

===Isometries===

The Mobius strip seems to have no nontrivial isometry.
==Curvatures==

==Properties==

{{nonorientable surface}}

The Mobius strip is a nonorientable surface. Thus, any compactification of it is also nonorientable. Hence, from the fact that [[orientable equals 3-embeddable|for compact surfaces orientability is equivalent to embeddability]] in [itex]\R^3[/itex], we conclude that no compactification of the Mobius strip can be embedded in [itex]\R^3[/itex].

{{negatively curved surface}}

From the curvature computations above, it is clear that the Gaussian curvature of the Mobius strip is everywhere negative.

{{ruled surface}}

At every point on the Mobius strip, it is possible to draw a lien segment containing that point that lies entirely on the Mobius strip.