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arXiv · 2010.09408

Intriguing Invariants of Centers of Ellipse-Inscribed Triangles

Mark Helman·Ronaldo Garcia·Dan Reznik
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Abstract

We describe invariants of centers of ellipse-inscribed triangle families with two vertices fixed to the ellipse boundary and a third one which sweeps it. We prove that: (i) if a triangle center is a fixed affine combination of barycenter and orthocenter, its locus is an ellipse; (ii) and that over the family of said affine combinations, the centers of said loci sweep a line; (iii) over the family of parallel fixed vertices, said loci rigidly translate along a second line. Additionally, we study invariants of the envelope of elliptic loci over combinations of two fixed vertices on the ellipse.

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Mark Helman, Ronaldo Garcia, Dan Reznik. 2020-10-19. Intriguing Invariants of Centers of Ellipse-Inscribed Triangles. https://doi.org/10.1007/s00022-021-00586-3

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