Infinite regular hexagon sequences on a triangle. (English) Zbl 0966.51013

Smith, Alvy Ray

Exp. Math. 9, No. 3, 397-406 (2000).

Starting with the inner and outer Napoleon triangle of a given triangle ABC, the author considers related infinite sequences leading to (more general) infinite sequences of regular hexagons corresponding with ABC, too. Then he defines a related hexagon-to-hexagon transform and investigates its algebraic properties, yielding further interesting geometric results.
The author underlines that experimentations with an educational program inspired the obtained results, whose proofs are based on eigenvector analysis of polygons in the complex plane.

Reviewer: Horst Martini (Chemnitz)

MSC:

51M04

Elementary problems in Euclidean geometries

Keywords:

Napoleon’s theorem; eigenvector; complex plane; hexagons

Software:

Geometer's Sketchpad

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[11]	DOI: 10.2307/2324901 · Zbl 0756.51017 · doi:10.2307/2324901