# Extremal polygons in R^3

@article{Panina2012ExtremalPI, title={Extremal polygons in R^3}, author={Gaiane Panina}, journal={arXiv: Geometric Topology}, year={2012} }

The oriented area function $A$ is (generically) a Morse function on the space of planar configurations of a polygonal linkage. We are lucky to have an easy description of its critical points as cyclic polygons and a simple formula for the Morse index of a critical point. However, for planar polygons, the function $A$ in many cases is not a perfect Morse function. In particular, for an equilateral pentagonal linkage it has one extra local maximum (except for the global maximum) and one extra…

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