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Journal for Geometry and Graphics 21 (2017), No. 2, 179--192
Copyright Heldermann Verlag 2017

Geometry and Design of Hexagonal Spirals (Voronoi and Other)

Konstantinos Myrianthis
58 Zan Moreas Street, Athens 15231, Greece

The geometry of equiangular spirals, i.e., discretized logarithmic spirals, never ceases to attract interest in the broad mathematical world where professionals and amateurs belong to. Voronoi and general hexagonal spiral systems have the unique attraction of offering opportunities for research with interesting results in geometry as well as in botany. The aim of the present work is to study the geometrical characteristics of such systems using synthetic and analytic methods.

Keywords: Spiral system, spiral phyllotaxis, quadrangular spiral system, hexagonal spiral system, Voronoi tiling, Voronoi cell, Delaunay triangulation.

MSC: 51M04; 51N20, 97M60

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