The involute of a circle
If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the interactive figure below, the unwound portion of the string is tangent to the circle at point Q, and in the radian measure of the angle measured from the positive -axis.
Either drag point Q along the circle, or press the play button in the lower left corner.
Developed for use with Thomas' Calculus, published by Pearson.