Quadrangles inscribed in a closed curve
The article investigates when four points of a quadrangle in the plane can be moved by a similarity such that they lie on a given Jordan curve. The main result states that for any planar \(C^2\) smooth starlike Jordan curve and any four points on a circle there exists a similarity that maps the four points to points of the Jordan curve, provided the curve intersects the circle in at most four points. The author shows that this problem is related to a certain problem on the sphere. This problem then can be solved with rather elementary methods.
scientific article; zbMATH DE number 846466