If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end [i]P[/i] traces an [i]involute[/i] of the circle. In the interactive figure below, the unwound portion of the string is tangent to the circle at point [i]Q, [/i]and [math]t[/math] in the radian measure of the angle measured from the positive [math]x[/math]-axis.[br][br]Either drag point [i]Q[/i] along the circle, or press the play button in the lower left corner.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]