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Mat. Sb., 2004, Volume 195, Number 2, Pages 3–16 (Mi msb798)  

This article is cited in 3 scientific papers (total in 3 papers)

Galois groups of the Heron–Sabitov polynomials for inscribed pentagons

V. V. Varfolomeev

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: The Galois groups of the $d$-, the $r$-, and the $S$-polynomials over fields of rational functions of the sides of a pentagon are calculated. These polynomials have the zeros at the diagonals, the radii of circumscribed circles, and the areas of inscribed polygons, respectively. The Galois groups turn out to be as large as possible. Elementary geometric applications are presented.

DOI: https://doi.org/10.4213/sm798

Full text: PDF file (245 kB)
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English version:
Sbornik: Mathematics, 2004, 195:2, 149–162

Bibliographic databases:

UDC: 513.7
MSC: 51M25, 12F10
Received: 09.06.2003

Citation: V. V. Varfolomeev, “Galois groups of the Heron–Sabitov polynomials for inscribed pentagons”, Mat. Sb., 195:2 (2004), 3–16; Sb. Math., 195:2 (2004), 149–162

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pak I., “The area of cyclic polygons: Recent progress on Robbins' conjectures”, Adv. in Appl. Math., 34:4 (2005), 690–696  crossref  mathscinet  zmath  isi
    2. Fedorchuk M., Pak I., “Rigidity and polynomial invariants of convex polytopes”, Duke Math. J., 129:2 (2005), 371–404  crossref  mathscinet  zmath  isi  elib
    3. Connelly R., “Comments on generalized Heron polynomials and Robbins' conjectures”, Discrete Math., 309:12 (2009), 4192–4196  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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