# Mapping the unit interval onto circles maintaining length

- Author:
- John Wayland Bales

Move the value of between values of 0 and using the slider and watch P trace out a path along the polar graph .
P also lies on the circle with center and radius .
Furthermore, the length of the arc from O to P always has length 1.

Prove the relationships described above. You want to consider using the law of sines on the isosceles triangle OPC where C is the center of the circle. The center C will change as changes.