Two circles of the same size are tangent to each other in a plane. One of the circles stays fixed and the other circle rolls around the first circle one time. How many times does the rolling circle turn around its center?

A super fun, and easy to state problem. Here’s our first run through it (FamilyMath 23 – sheesh – we are over 250 now!!):

Well . . . today I ran across the same problem in our Introduction to Geometry book. Fun to see the ideas the the boys have 3 years later: