A trichotomy for rectangles inscribed in Jordan loops (Q2196649)

By proving a general structural theorem about rectangles inscribed in a Jordan loop (the image of the circle under a continuous injective map into the plane), the author deduces as corollaries the facts that all but at most 4 points of any Jordan loop are vertices of inscribed rectangles, and that a Jordan loop has an inscribed rectangle of every aspect ratio if it has 3 points which are not vertices of inscribed rectangles.