Invariant Center Power and Elliptic Loci of Poncelet Triangles
| Autor: | Dan Reznik, Dominique Laurain, Ronaldo Garcia, Mark Helman |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Control and Optimization Dynamical Systems (math.DS) Computer Science::Computational Geometry Concentric Ellipse Combinatorics Computer Science - Robotics symbols.namesake Computer Science - Graphics Mathematics - Metric Geometry FOS: Mathematics Mathematics::Metric Geometry Center (algebra and category theory) Complex Variables (math.CV) Mathematics - Dynamical Systems 51M04 51N20 51N35 68T20 Circumscribed circle Invariant (mathematics) Linear combination Mathematics Numerical Analysis Algebra and Number Theory Mathematics - Complex Variables Metric Geometry (math.MG) Graphics (cs.GR) Control and Systems Engineering Euler's formula symbols Robotics (cs.RO) Triangle center |
| Zdroj: | Journal of Dynamical and Control Systems. 29:157-184 |
| ISSN: | 1573-8698 1079-2724 |
| DOI: | 10.1007/s10883-021-09580-z |
| Popis: | We study center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. We show that (i) for any concentric pair, the power of the center with respect to either circumcircle or Euler's circle is invariant, and (ii) if a triangle center of a 3-periodic in a generic nested pair is a fixed affine combination of barycenter and circumcenter, its locus over the family is an ellipse. 25 pages, 16 figures, 6 tables, 8 video links, 7 live app links |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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