Möbius strip coordinates

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)