Loci of 3-periodics in an Elliptic Billiard: Why so many ellipses?
نویسندگان
چکیده
A triangle center such as the incenter, barycenter, etc., is specified by a function thrice- and cyclically applied on sidelengths and/or angles. Consider 1d family of 3-periodics in elliptic billiard, loci its centers. Some will sweep ellipses, others higher-degree algebraic curves. We propose two rigorous methods to prove if locus given an ellipse: one based computer algebra, another algebro-geometric method. also that rational sidelengths, algebraic.
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We thank the Russell Sage Foundation for their generous support of this research.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2023
ISSN: ['1095-855X', '0747-7171']
DOI: https://doi.org/10.1016/j.jsc.2022.06.001