Geodesic
Galois groups of the Heron--Sabitov polynomials for inscribed pentagons
Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 149-162

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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. 
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     author = {V. V. Varfolomeev},
     title = {Galois groups of the {Heron--Sabitov}  polynomials for inscribed pentagons},
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     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_2_a0/}
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V. V. Varfolomeev. Galois groups of the Heron--Sabitov  polynomials for inscribed pentagons. Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 149-162. http://geodesic.mathdoc.fr/item/SM_2004_195_2_a0/