Squares Found in Curves

The Prompt

Draw or generate five distinct simple closed curves of varying character — convex, smooth, piecewise-linear, and at least one with an irregular or jagged boundary. For each curve, find (by measurement, construction, or computation) four points that form an inscribed square, or attempt to and document the difficulty. Record the curves, the inscribed squares found, and a reflection on which classes of curves made the search easy and which made it hard.

Completion Criteria

The five curves (drawn or computed), the inscribed squares found (or a documented account of the attempt), and a one-paragraph reflection on the variation in difficulty.

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