Abstract.
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 a1, ..., 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pinelis, I. Cyclic polygons with given edge lengths: Existence and uniqueness. J. geom. 82, 156–171 (2005). https://doi.org/10.1007/s00022-005-1752-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00022-005-1752-8