Cyclic polygons are critical points of area
- First Online:
- 37 Downloads
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.
Unable to display preview. Download preview PDF.
- 1.V. Arnold, A. Varchenko, and S. Gusein-Zade, Singularities of Differentiable Mappings [in Russian], Nauka, Moscow (2005).Google Scholar
- 3.R. Connelly and E. Demaine, “Geometry and topology of polygonal linkages,” in: Handbook of Discrete and Computational Geometry, 2nd edition, CRC Press, Boca Raton (2004), pp. 197–218.Google Scholar
- 4.H. Coxeter and S. Greitzer, Geometry Revisited, Amer. Math. Soc. (1967).Google Scholar
- 5.E. Elerdashvili, M. Jibladze, and G. Khimshiashvili, “Cyclic configurations of pentagon linkages,” Bull. Georgian Nat. Acad. Sci., 2, No. 4, 13–16 (2008).Google Scholar
- 10.G. Khimshiashvili, “On configuration spaces of planar pentagons,” Zap. Nauchn. Semin. POMI, 292, 120–129 (2002).Google Scholar
- 11.G. Khimshiashvili, “Signature formulae and configuration spaces,” J. Math. Sci. 59 (2009), in press.Google Scholar