Associated curves

Time was, people learned about evolutes and involutes, and caustics,
and other associated curves to given plane curves.

These days have passed (except for Maxim, who still teaches that to
his students): these are pretty but not very useful.
Some such games are useful in optics, especially caustics, but in
general, these classical (and motivating! the founders of calc
studied these things!) constructions have not proven to be useful or
interesting: they're eccentric beauties, but haven't depth.
(unlike the platonic solids, say, which lead to group theory).
