MathDB
Circle rolling around another n times.

Source:

January 25, 2011
floor functiongeometry unsolvedgeometry

Problem Statement

A circle of radius 11 rolls around a circle of radius 2\sqrt{2}. Initially, the tangent point is colored red. Afterwards, the red points map from one circle to another by contact. How many red points will be on the bigger circle when the center of the smaller one has made nn circuits around the bigger one?