The Circumbilliard: Any Triangle can be a 3-Periodic
arXiv:2004.06776v12 citations
Originality Synthesis-oriented
AI Analysis
This work addresses a geometric problem in mathematics, specifically in the study of periodic orbits and conics, and appears incremental as it builds on known concepts of circumconics and billiards.
The paper tackles the problem of identifying a circumellipse (Circumbilliard) for any triangle such that the triangle is a 3-periodic orbit, and it characterizes the properties and loci associated with this ellipse.
A Circumconic passes through a triangle's vertices. We define the Circumbilliard, a circumellipse to a generic triangle for which the latter is a 3-periodic. We study its properties and associated loci.