Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 15 (2008), No. 2, 411--426
Copyright Heldermann Verlag 2008

An Evolutionary Structure of Convex Quadrilaterals

Anastasios N. Zachos
Dept. of Mathematics, University of Patras, 26500 Rion, Greece

Gerasimos Zouzoulas
Meintani 25, 117-41 Athens, Greece

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.

Keywords: Fermat-Torricelli problem, inverse Fermat-Torricelli problem, generalized convex quadrilaterals.

MSC: 51E12, 52A10, 52A55, 51E10

[ Fulltext-pdf  (1973  KB)] for subscribers only.