Brahmagupta formula for cyclic quadrilaterals in the hyperbolic plane

A. D. Mednykh

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 247-255.

Résumé

The Heron formula relates the area of an Euclidean triangle to its side lengths. Indian mathematician and astronomer Brahmagupta, in the seventh century, gave the analogous formulas for a convex cyclic quadrilateral. Several non-Euclidean versions of the Heron theorem have been known for a long time. In this paper we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of an equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmahupta formula for such quadrilaterals.

Détail

Keywords: Brahmagupta formula, hyperbolic quadrilateral.
Mots-clés : Heron formula, cyclic polygon

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