[bobby_table]

The way I think of this is: If instead of having a small circle rolling around a larger one, think of a circle with ANY non-zero radius rolling around one with a zero (or really really small) radius. You’ll always end up with at least one rotation, regardless of how small the other circle is. So +1 makes sense.

[saberdancer]

The way I thought about it, you have to roll around the larger one and you have to roll around yourself (+1). So if they are two same size circles, it's 1 for the other and 1 for yourself. If the other one has 3 times bigger radius, it is 3 for the bigger one and 1 for yourself. Etc.

Not sure if it is mathematically accurate but it seemed to make sense to me.