Intriguing Invariants of Centers of Ellipse-Inscribed Triangles
| Autor: | Mark Helman, Dan Reznik, Ronaldo Garcia |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Boundary (topology) Metric Geometry (math.MG) Center (group theory) Ellipse Combinatorics Computer Science - Robotics 53A04 51M04 51N20 Affine combination Mathematics - Metric Geometry Line (geometry) FOS: Mathematics Computer Science - Computational Geometry Geometry and Topology Affine transformation Envelope (mathematics) Robotics (cs.RO) Inscribed figure Mathematics |
| DOI: | 10.48550/arxiv.2010.09408 |
| Popis: | 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. Comment: 17 pages, 10 figures, 3 tables, 6 video links |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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