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arXiv · 2401.13002

Theorem Discovery Amongst Cyclic Polygons

Philip Todd
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Abstract

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.

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Philip Todd. 2024-01-22. Theorem Discovery Amongst Cyclic Polygons. https://doi.org/10.4204/eptcs.398.18

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