Cyclic polygons with given edge lengths: Existence and uniqueness
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.
Journal of Geometry
Cyclic polygons with given edge lengths: Existence and uniqueness.
Journal of Geometry,
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