Category:Möbius Strip
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This category contains results about Möbius Strip.
Definitions specific to this category can be found in Definitions/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.
Pages in category "Möbius Strip"
This category contains only the following page.