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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13002 |
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| _version_ | 1866914651173814272 |
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| author | Todd, Philip |
| author_facet | Todd, Philip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theorem Discovery Amongst Cyclic Polygons Todd, Philip Computational Geometry Artificial Intelligence 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. |
| title | Theorem Discovery Amongst Cyclic Polygons |
| topic | Computational Geometry Artificial Intelligence |
| url | https://arxiv.org/abs/2401.13002 |