[symmetricsaurus]

Yes I’m thinking in terms of different frames of reference.

Imagine that you’re a tiny ant that lives on the large circle. When you push the small circle around the large circle you will see it make four rotations before you get back to the starting point. This is the local frame of reference.

Now imagine you’re a giant living in the space with the circles. You see the small circle do five full rotations. Four are the same that the ant sees but you also see the ant itself do one rotation simultaneously as it walks along the large circle making five in total.

It would be more accurate to say that you have 4 local rotations and that the local frame rotates one full turn in the global frame.

Does this make sense to someone with a high-school level of geometry knowledge? Not as I wrote it I initially (but there was no such goal). The analogy with the giant and the ant together with some nice illustrations maybe?