Two pins and a taut string trace an ellipse — and so do several unrelated machines. The string secretly encodes one rule: the sum of distances to the foci is constant. Add a third pin and that rule stops giving a clean ellipse (you get an n-ellipse), while the taut string traces the convex-hull-perimeter locus instead. Swap sum for product and you get Cassini ovals: a blob that pinches into a figure-eight, then splits in two.