I have a circle and a line with the length of its circumference. One end of the line is attached to a point on the circle circumference, forming the shape of the lowercase 'b'. Now, the line begins to wrap the circle clockwise, until it completes one revolution around the circle, where there's no more "line".
What is the path created by the free end of the line?
The name you are looking for is involute of a circle.