Theorem Discovery Amongst Cyclic Polygons
This work addresses theorem discovery in geometry, specifically for cyclic polygons, but it is incremental as it builds on known geometric properties without introducing a new paradigm.
The paper tackles the problem of discovering geometric theorems for cyclic polygons by proving that a linear combination of angles between specific side pairs is constant, and it presents a program to generate new geometry proof problems and solutions based on this result.
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.