It is shown that typical critical points of the signed area function on the moduli space of a generic planar polygon are given by cyclic configurations, i.e., configurations that can be inscribed in a circle. Several related problems are briefly discussed in conclusion. Bibliography: 14 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 238–245.
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Panina, G., Khimshiashvili, G. Cyclic polygons are critical points of area. J Math Sci 158, 899–903 (2009). https://doi.org/10.1007/s10958-009-9417-z
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DOI: https://doi.org/10.1007/s10958-009-9417-z