Affine regular polygons (Q950670)

The propeller theorem says that, given three equilateral triangles with one common vertex, the midpoints of the segments connecting the free neighbouring vertices form an equilateral triangle. The author generalizes this theorem by replacing the given triangles by affine images of regular \(n\)-gons or even star-polygons. His proofs are based on multiple applications of rotations and trigonometric relations. The paper contains also a related extension of Napoleon's theorem.