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Journal for Geometry and Graphics 12 (2008), No. 2, 151--160
Copyright Heldermann Verlag 2008

Computation with Pentagons

Pavel Pech
Pedagogical Faculty, University of South Bohemia, Jeronymova 10, Ceske Budejovice, Czech Republic

The paper deals with properties of pentagons in a plane which are related to the area of a pentagon. First the formulas of Gauss and Monge holding for any pentagon in a plane are studied. Both formulas are derived by the theory of automated theorem proving. In the next part the area of cyclic pentagons is investigated. On the base of the Nagy-Rédey theorem and other results, the formula for the area of a cyclic pentagon which is given by its side lengths is rediscovered. This is the analogue of well-known Heron and Brahmagupta formulas for triangles and cyclic quadrilaterals. The method presented here could serve as a tool for solving this problem for cyclic n-gons for a higher n.

Keywords: Area of a cyclic pentagon, Monge formula, Gauss formula, Groebner bases of ideals.

MSC: 51M25; 51N20, 52A38

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