Geodesic
An Evolutionary Structure of Convex Quadrilaterals
Journal of convex analysis, Tome 15 (2008) no. 2, pp. 411-426.

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

We solve the problem of the evolution of convex quadrilaterals by applying the inverse weighted Fermat-Torricelli problem, the invariance property of the weighted Fermat-Torricelli point in the plane R2, two-dimensional sphere S2 and the two-dimensional hyperboloid H2. This means that the property of plasticity is inherited by some evolutionary convex quadrilaterals. An important application is the connection of the Fermat-Torricelli point with the fundamental equation of P. de Fermat.
Classification : 51E12, 52A10, 52A55, 51E10
Mots-clés : Fermat-Torricelli problem, inverse Fermat-Torricelli problem, generalized convex quadrilaterals 
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     title = {An {Evolutionary} {Structure} of {Convex} {Quadrilaterals}},
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A. N. Zachos; G. Zouzoulas. An Evolutionary Structure of Convex Quadrilaterals. Journal of convex analysis, Tome 15 (2008) no. 2, pp. 411-426. http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a15/