The well-known dual pair of Napoleon equilateral triangles intrinsic to each triangle is extended to infinite sequences of them, shown to be special cases of infinite regular hexagon sequences on each triangle. A set of hexagon-to-hexagon transformations, the hex operators, is defined for this purpose, a set forming an abelian monoid under function composition. The sequences result from arbitra...

Medycyna Nowożytna » Tom 28 (2022) Zeszyt 1 „Prokrustowe łoże” – i coś więcej. Jean-Claude Dammame, Å»ołnierze Wielkiej Armii, Napoleon V, Oświęcim 2016 A

The Euler reflection point E of a triangle is known in literature as the common point of the reflections of its Euler line OH in each of its sidelines, where O and H are the circumcenter and the orthocenter of the triangle, respectively. In this note we prove that E lies on six circles associated with the triangles of Napoleon.