Cyclic polygons with given edge lengths: Existence and uniqueness

Document Type


Publication Date



Let a1, ..., a n be positive numbers satisfying the condition that each of the a i 's is less than the sum of the rest of them; this condition is necessary for the a i 's to be the edge lengths of a (closed) polygon. It is proved that then there exists a unique (up to an isometry) convex cyclic polygon with edge lengths a 1, ..., a n . On the other hand, it is shown that, without the convexity condition, there is no uniqueness-even if the signs of all central angles and the winding number are fixed, in addition to the edge lengths. © Birkhäuser Verlag, Basel, 2005.

Publication Title

Journal of Geometry