A Method for the Automated Discovery of Angle Theorems

TL;DR

This paper introduces a generalized graph-theoretic approach to automate the discovery of angle theorems by analyzing linear systems derived from geometric configurations.

Contribution

It extends the Naive Angle Method with a graph-based generalization, enabling automated theorem discovery in angle geometry.

Findings

Successfully generalizes the matrix structure for various geometric theorems

Provides a framework for automated discovery of angle theorems

Enhances the Naive Angle Method with graph theory techniques

Abstract

The Naive Angle Method, used by Geometry Expressions for solving problems which involve only angle constraints, represents a geometrical configuration as a sparse linear system. Linear systems with the same underlying matrix structure underpin a number of different geometrical theorems. We use a graph theoretical approach to define a generalization of the matrix structure.