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Journal of Convex Analysis 22 (2015), No. 4, 1091--1106
Copyright Heldermann Verlag 2015

A Creation Principle of some Fish Type Skeletons in the Sense of Leibniz

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

We create some fish type skeletons in the two dimensional Euclidean Space which is composed of seven evolutionary schemes and they are derived by applying a plasticity principle of convex pentagons and quadrilaterals, the generalized plasticity of polygons which is obtained by splitting the weights along the main bone of the skeleton and the plasticity of some generalized Gauss trees via the creation principle of a Fermat-Torricelli tree structure of degree four. Leibniz perception of a fish type structure is accomplished via a parallel translation of the branches (bones) of the skeleton between the weighted Fermat-Torricelli points of degree at most four which have been created by the generalized geometric plasticity along the main bone of the skeleton.

Keywords: Weighted Fermat-Torricelli tree structure, Steiner minimal tree, convex pentagons, plasticity principle, degree of plasticity.

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

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