I was just thinking about a problem for fun where n layers of tape of thickness t are wound on a spool of inner radius r and one needs to find the the variation of angular speed of spool as a function of time such that tape is obtained at a constant time rate v. But , my question is , what kind of a curve is the spiral? To , me , at the first glance , it look like a discrete function. Then some googling tells me it could be an archimedes spiral. Few more suggest an involute circle. Also , can anyone explain to me why its not a discrete function? I have trouble visualizing this. Some inputs would be appreciated.