Geodesic
Computation with Pentagons
Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 151-16.

Voir la notice de l'article provenant de la source Heldermann Verlag

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-R�dey 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.
Classification : 51M25, 51N20, 52A38
Mots-clés : Area of a cyclic pentagon, Monge formula, Gauss formula, Groebner bases of ideals 
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     author = {P. Pech },
     title = {Computation with {Pentagons}},
     journal = {Journal for geometry and graphics},
     pages = {151--16},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a3/}
}
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P. Pech . Computation with Pentagons. Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 151-16. http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a3/