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Cyclic polygons are critical points of area. (English. Russian original) Zbl 1193.52015

J. Math. Sci., New York 158, No. 6, 899-903 (2009); translation from Zap. Nauchn. Semin. POMI 360, 238-245 (2008).
Summary: 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.

MSC:

52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
05B30 Other designs, configurations
55R80 Discriminantal varieties and configuration spaces in algebraic topology
57R20 Characteristic classes and numbers in differential topology
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