Deformations of Planar Equilateral Polygons with a Constant Index
https://doi.org/10.18255/1818-1015-2013-1-138-159
Abstract
A carpenter’s rule problem is considered for the case of a self-intersecting planar polygon with additional restriction: the index (turning number) of the polygon should be preserved during deformation. We present a solution for equilateral polygons and state a problem for general ones.
About the Author
E. S. Zaputryaeva
Moscow State Pedagogical University
Russian Federation
Russian Federation
аспирант,
107140, Russia, Moscow, Krasnoprudnaya st., 14
References
1. Connelly R., Demaine E., Rote G. Straightening polygonal arcs and convexifying polygonal cycles // Discrete and Computational Geometry. 2003. V. 30 (5). P. 205–239.
2. Lenhart W. J., Whitesides S. Reconfiguring closed polygonal chains in Euclidian d-space // Discrete and Computational Geometry. 1995. V. 13. P. 123–140.
3. Streinu I. A combinatorial approach to planar non-colliding robot arm motion planning // In ACM/IEEE Symposium on Foundations of Computer Science. 2000. P. 443–453.
4. Сабитов И.Х. Чему равна сумма углов многоугольника? // КВАНТ. 2001. № 3. С. 7–12. (Sabitov I. Kh. Chemu ravna summa uglov mnogougol’nika? // KVANT. 2001. No. 3. P. 7–12 [in Russian]).
5. Сабитов И.Х. Вокруг доказательства леммы Лежандра – Коши о выпуклых многоугольниках // Сибирский математический журнал. 2004. Т. 45, № 4. С. 892 – 919. (English transl.: Sabitov I. Kh. Around the Proof of the Legendre – Cauchy Lemma on Convex Polygons// Siberian Mathematical Journal. 2004. V. 45, No. 4. P. 740–762) .
Review
For citations:
Zaputryaeva E.S. Deformations of Planar Equilateral Polygons with a Constant Index. Modeling and Analysis of Information Systems. 2013;20(1):138-159. (In Russ.) https://doi.org/10.18255/1818-1015-2013-1-138-159
Views:
887
Email this article 