Journal of Mathematical Sciences

, Volume 158, Issue 6, pp 899-903

First online:

Cyclic polygons are critical points of area

  • G. PaninaAffiliated withInstitute for Informatics and Automation Email author 
  • , G. KhimshiashviliAffiliated withIlia Chavchavadze State University

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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.