Piero’s theorem

Piero's theorem states that if a point moves along a circle while maintaining a constant distance from a fixed point inside the circle, then the trajectory of that point forms a special shape called an involute of the circle. In other words, the path traced by a point attached to a taut string unwound from the circle's edge is related to the circle itself through a precise geometric relationship. This theorem helps us understand the geometric connections between circles and their associated curves, and has applications in areas like gear design and the study of rolling motions.