Changes

Jump to: navigation, search

Mobius strip

1,345 bytes added, 09:22, 1 August 2007
no edit summary
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==
<math>(x,1) \sim (-x,-1), (1,y) \sim (-1,y)</math>
{{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 <math>\R^3</math>, we conclude that no compactification of the Mobius strip can be embedded in <math>\R^3</math>.
 
{{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.
Bureaucrats, emailconfirmed, Administrators
184
edits

Navigation menu