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On the area of a polygonal linkage. / Panina, G. Yu; Khimshiashvili, G. N.

In: Doklady Mathematics, Vol. 85, No. 1, 01.02.2012, p. 120-121.

Research output: Contribution to journal › Article › peer-review

Harvard

Panina, GY & Khimshiashvili, GN 2012, 'On the area of a polygonal linkage', Doklady Mathematics, vol. 85, no. 1, pp. 120-121. https://doi.org/10.1134/S1064562412010401

APA

Panina, G. Y., & Khimshiashvili, G. N. (2012). On the area of a polygonal linkage. Doklady Mathematics, 85(1), 120-121. https://doi.org/10.1134/S1064562412010401

Vancouver

Panina GY, Khimshiashvili GN. On the area of a polygonal linkage. Doklady Mathematics. 2012 Feb 1;85(1):120-121. https://doi.org/10.1134/S1064562412010401

Author

Panina, G. Yu ; Khimshiashvili, G. N. / On the area of a polygonal linkage. In: Doklady Mathematics. 2012 ; Vol. 85, No. 1. pp. 120-121.

BibTeX

@article{9f58e7dd800e4427aec85a16497bc978,
title = "On the area of a polygonal linkage",
abstract = "A study was conducted to investigate the critical points of oriented area regarded as a function on the moduli space of a polygonal linkage. Jacob Steiner showed that the area of a polygon with fixed edge lengths attained its maximum at the cyclic polygon. Physically, a polygonal linkage was interpreted as a set of cyclically joined rigid rods of length l i. Free bending and self-intersections, along with self-overlaps of edges were allowed at the locations of joints. Theorem 1 stated that the set of A critical points coincided with the set of all cyclic configurations for any generic polygonal linkage. This theorem was proved by Steiner's four-hinge method, which consisted in fixing n - 2 vertices of the configuration and considering the bendings generated by the quadrangular linkage.",
author = "Panina, {G. Yu} and Khimshiashvili, {G. N.}",
year = "2012",
month = feb,
day = "1",
doi = "10.1134/S1064562412010401",
language = "English",
volume = "85",
pages = "120--121",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "1",

}

RIS

TY - JOUR

T1 - On the area of a polygonal linkage

AU - Panina, G. Yu

AU - Khimshiashvili, G. N.

PY - 2012/2/1

Y1 - 2012/2/1

N2 - A study was conducted to investigate the critical points of oriented area regarded as a function on the moduli space of a polygonal linkage. Jacob Steiner showed that the area of a polygon with fixed edge lengths attained its maximum at the cyclic polygon. Physically, a polygonal linkage was interpreted as a set of cyclically joined rigid rods of length l i. Free bending and self-intersections, along with self-overlaps of edges were allowed at the locations of joints. Theorem 1 stated that the set of A critical points coincided with the set of all cyclic configurations for any generic polygonal linkage. This theorem was proved by Steiner's four-hinge method, which consisted in fixing n - 2 vertices of the configuration and considering the bendings generated by the quadrangular linkage.

AB - A study was conducted to investigate the critical points of oriented area regarded as a function on the moduli space of a polygonal linkage. Jacob Steiner showed that the area of a polygon with fixed edge lengths attained its maximum at the cyclic polygon. Physically, a polygonal linkage was interpreted as a set of cyclically joined rigid rods of length l i. Free bending and self-intersections, along with self-overlaps of edges were allowed at the locations of joints. Theorem 1 stated that the set of A critical points coincided with the set of all cyclic configurations for any generic polygonal linkage. This theorem was proved by Steiner's four-hinge method, which consisted in fixing n - 2 vertices of the configuration and considering the bendings generated by the quadrangular linkage.

UR - http://www.scopus.com/inward/record.url?scp=84858419833&partnerID=8YFLogxK

U2 - 10.1134/S1064562412010401

DO - 10.1134/S1064562412010401

M3 - Article

AN - SCOPUS:84858419833

VL - 85

SP - 120

EP - 121

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -

ID: 49857076