Abstract

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\mathbb{R}^2, two-dimensional sphere S2S^2 and the two-dimensional hyperboloid H2H^2. 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.

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Keywords

  • Fermat-Torricelli problem
  • inverse Fermat-Torricelli problem
  • generalized convex quadrilaterals

Mathematics Subject Classification

51E12, 52A10, 52A55, 51E10

References

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Suggested citation

A. N. Zachos, G. Zouzoulas. “An Evolutionary Structure of Convex Quadrilaterals.” Journal of Convex Analysis 15 (2008), No. 2, 411–426. https://doi.org/10.68381/jca15029

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.