Symmedians as hyperbolic barycenters

DOI10.5802/crmath.677MaRDI QIDQ6644102

Maxim Arnold, Carlos E. Arreche

Publication date: 27 November 2024

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

symmedian pointharmonic polygonhyperbolic barycenterideal hyperbolic polygon

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Spherical and hyperbolic convexity (52A55) Geometric constructions in real or complex geometry (51M15) Incidence structures embeddable into projective geometries (51A45) Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30) Discrete differential geometry (53A70)

Cites Work

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• Circumcenter of mass and generalized Euler line
• Characterizing centers of convex bodies via optimization
• Early history of the symmedian point.
• A new method for the investigation of harmonic polygons.
• A hyperbolic view of the seven circles theorem
• Poncelet Porisms and Beyond
• Hyperbolic Geometry on a Hyperboloid
• An Algebraic Method to Find the Symmedian Point of a Triangle
• The Limit Point of the Pentagram Map
• The Limit Point of the Pentagram Map and Infinitesimal Monodromy
• Cross-ratio Dynamics on Ideal Polygons

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