This article is cited in 5 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.

UDC: 513.7

MSC: 51M25, 12F10

Received: 09.06.2003

DOI: 10.4213/sm798

 English version: Sbornik: Mathematics, 2004, 195:2, 149–162

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