Cyclic polygons with given edge lengths: Existence and uniqueness
Document Type
Article
Publication Date
8-2005
Department
Department of Mathematical Sciences
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 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.
Publication Title
Journal of Geometry
Recommended Citation
Pinelis, I.
(2005).
Cyclic polygons with given edge lengths: Existence and uniqueness.
Journal of Geometry,
82(1-2), 156-171.
http://doi.org/10.1007/s00022-005-1752-8
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4627
