循环多边形中的定理发现

arXiv - CS - Mathematical Software Pub Date : 2024-01-22 DOI:arxiv-2401.13002

Philip ToddSaltire Software

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引用次数: 0

摘要

我们研究了关于循环 2n 边形的一类几何定理。我们证明，如果取 n 对互不相交的边，每对边之间隔着偶数条多边形边，那么这些边之间的角的线性组合是常数。我们给出了线性组合的公式，并用这些角给出了定理说明。我们描述了一个程序，该程序利用这一结果生成新的几何证明问题及其解答。

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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.

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arXiv - CS - Mathematical Software

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