Cramer-Castillon on a Triangle's Incircle and Excircles
Dominique Laurain, Peter Moses, Dan Reznik
TL;DR
This paper investigates the Cramer-Castillon problem for triangles, focusing on inscribed polygons passing through specified points on the incircle and excircles, expanding understanding of geometric configurations.
Contribution
It provides new insights into the existence and properties of polygons inscribed in a triangle's incircle and excircles passing through given points.
Findings
Characterization of inscribed polygons passing through specified points
Conditions for existence of such polygons
New geometric properties related to incircle and excircles
Abstract
The Cramer-Castillon problem (CCP) consists in finding one or more polygons inscribed in a circle such that their sides pass cyclically through a list of points. We study this problem where the points are the vertices of a triangle and the circle is either the incircle or excircles.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematics and Applications · Advanced Differential Equations and Dynamical Systems