My 16 year old son caught me with this last night & I marched straight into the incomplete response, but fairly quickly rebutted that the smaller circle does in fact revolve only [ratio] times in the radial space, but I conceded that a complete response would be to add that it revolves [ratio] + 1 times in the Cartesian space (after he clarified my assumption for me). I'll also concede that my retort was a complete reaction, but it now has me wondering if there are legitimate space-transformations to clarify the distinction?

## Space & Co-ordinates

My 16 year old son caught me with this last night & I marched straight into the incomplete response, but fairly quickly rebutted that the smaller circle does in fact revolve only [ratio] times in the radial space, but I conceded that a complete response would be to add that it revolves [ratio] + 1 times in the Cartesian space (after he clarified my assumption for me). I'll also concede that my retort was a complete reaction, but it now has me wondering if there are legitimate space-transformations to clarify the distinction?