The Möbius strip coordinates calculator returns the x, y and z coordinates of a Möbius strip based on two values that indicate the distance along the Möbius strip (u) and the distance from the edge (v).
INSTRUCTIONS: Enter the following:
- (u) Length along the Möbius strip
- (v) Height above the edge of the Möbius strip
Möbius strip Coordinates (X, Y, Z): The calculator returns the coordinates as real numbers.
The Math / Science
A Möbius strip is a surface with only one side and only one boundary. The strip has the mathematical property of being non-orientable. It can be realized as a ruled surface.
The following formula is used to find the coordinates:
`x=(1+v/2cos(u/2))cosu`
`y=(1+v/2cos(u/2))sinu`
`z = v/2*sin(u/2)`
where:
- v = integer parameter that moves from one edge to the other
- u = integer parameter that runs around the strip
Wikipedia states that the formula creates a Möbius strip of width 1, whose center circle has radius 1, lies in the xy-plane and is centered at (0,0,0). The parameter u runs around the strip while v moves from one edge to the other.
References
Wikipedia (https://en.wikipedia.org/wiki/M%C3%B6bius_strip)