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A Web of Confocal Parabolas in a Grid of Hexagons (2112.02157v3)
Published 3 Dec 2021 in math.MG, cs.CG, cs.GR, cs.RO, and math.DS
Abstract: If one erects regular hexagons upon the sides of a triangle $T$, several surprising properties emerge, including: (i) the triangles which flank said hexagons have an isodynamic point common with $T$, (ii) the construction can be extended iteratively, forming an infinite grid of regular hexagons and flank triangles, (iii) a web of confocal parabolas with only three distinct foci interweaves the vertices of hexagons in the grid. Finally, (iv) said foci are the vertices of an equilateral triangle.