# Circle rolling on a circle [duplicate]

Consider a circle with radius 3. Rolling around this circle is another circle, with radius 1. How many times has the little circle made a full turn when it has returned to it´s starting point?

This was an SAT question that everyone got wrong. The supposed answer was 3, following the math of $\frac{2\pi{(3)}}{2\pi{(1)}}$, which would yield 3. But as the video shows, after just one quarter rotation, the rotating circle has completed one turn. It takes a full four turns for it to complete. In fact, the formula used is: When radius A is $1/n$ radius B, the number of rotations will be $n+1$.