arXiv subjects

Philip Todd

Publications and source records attributed to Philip Todd.

3 recordsLinked to original sources

arXiv2024

Theorem Discovery Amongst Cyclic Polygons

We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides which is constant. We present a formula for the linear combination, which provides a theorem statement in terms of those angles. We describe a program which uses this result to generate new geometry proof problems and their solutions.

cs.CG↗

arXiv2024

Using GXWeb for Theorem Proving and Mathematical Modelling

GXWeb is the free browser based version of the symbolic geometry software Geometry Expressions. We demonstrate its use in an educational setting with examples from theorem proving, mathematical modelling and loci and envelopes.

math.HO↗

arXiv2022

A Method for the Automated Discovery of Angle Theorems

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.

cs.SC↗