On the geometry of the ricochet locus
Jaydeep Chipalkatti

TL;DR
This paper explores the geometric properties of the ricochet configuration related to Pascal's theorem, including symmetry, defining equations, and algebraic structure, advancing understanding of its geometric and algebraic nature.
Contribution
It provides a geometric proof of Pascal line coincidence, computes the symmetry group, and characterizes the ricochet locus as a complete intersection of invariant hypersurfaces.
Findings
Proves Pascal line coincidence in R-configuration
Calculates the symmetry group of R-configuration
Determines the defining equations of the ricochet locus
Abstract
This paper is a study of the so-called `ricochet configuration' (or -configuration) which arises in the context of Pascal's theorem. We give a geometric proof of the fact that a specific pair of Pascal lines is coincident for a sextuple in -configuration. We calculate the symmetry group of a generic -configuration, as well as the degree of the subvariety of all such configurations. We also determine the -equivariant defining equations for , and show that it is an ideal-theoretic complete intersection of two invariant hypersurfaces.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory
