When I look up a curve on Wikipedia, I'll often see a lot of properties along the lines of "you can generate curve X by rolling a circle along curve Y and tracing the trajectory of a single point," or other things to similar effect. Of course the individual calculations are elementary, but are these just scattered facts or do these kinds of results belong to a useful general theory? So far as I know, these classical geometric concepts aren't taught in schools anymore.
Is there a good way to learn about these properties systematically? Or, conversely, a good reason why they are only of historical interest?