The most ridiculed idea in the history of astronomy — circles riding on circles — turns out to draw anything. Pick a shape, then drag the number of circles.
Each circle turns at a whole-number rate; a pen at the end of the chain traces the curve. Add more circles and the tracing sharpens. A circle needs one. A square's corners never fully settle — sharp turns cost infinitely many circles. That "cost of a corner" is the same fact that makes a JPEG blur an edge.