Journal of Mathematical Sciences

, Volume 158, Issue 6, pp 899–903

Cyclic polygons are critical points of area

Article

DOI: 10.1007/s10958-009-9417-z

Cite this article as:
Panina, G. & Khimshiashvili, G. J Math Sci (2009) 158: 899. doi:10.1007/s10958-009-9417-z

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.

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute for Informatics and AutomationSt. PetersburgRussia
  2. 2.Ilia Chavchavadze State UniversityTbilisiGeorgia