, Volume 9, Issue 2, pp 364-377
Date: 18 Feb 2011

Morse index of a cyclic polygon

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Abstract

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.