Category:Definitions/Möbius Strip

This category contains definitions related to Möbius Strip.
Related results can be found in Category:Möbius Strip.

A Möbius strip is a surface with boundary obtained by twisting a side of a rectangle by $180$ degrees, then joining the twisted side and the opposite side of it together.

Thus in the above diagram, $AB$ is identified with $CD$.

Formal Construction

Let $T$ be the square embedded in the Cartesian plane defined as:

$T = \closedint 0 1 \times \closedint 0 1$

Let $T'$ be the quotient space formed from $T$ using the identification mapping $p: T \to T'$ as follows:

$\forall \tuple {x, y} \in T: \map p {x, y} = \begin {cases} \tuple {1, 1 - y} & : x = 0 \\ \paren {x, y} & : x \ne 0 \end {cases}$

Then $T'$ is a Möbius strip.