Novel required properties of, and efficient algorithms to seek, perfect cuboids
Geombinatorics Quarterly, Volume XXXIII, Issue 3, p 107, (2024) We present a novel approach to the age-old question of whether perfect cuboids exist. Our approach consists of two new computer search algorithms, arising from the analysis of "perfect plinths" reported by one of us recently,...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
06.01.2024
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2401.06784 |
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| Abstract | Geombinatorics Quarterly, Volume XXXIII, Issue 3, p 107, (2024) We present a novel approach to the age-old question of whether perfect
cuboids exist. Our approach consists of two new computer search algorithms,
arising from the analysis of "perfect plinths" reported by one of us recently,
that are much more efficient than any prior algorithm of which we are aware.
Using this approach, we also (i) identify some new two-parameter families of
edge cuboids, and (ii) show that large proportions of aspect ratios of faces or
internal rectangles cannot be present in a perfect cuboid, a property that was
previously reported only for faces with the aspect ratio 4:3. |
|---|---|
| AbstractList | Geombinatorics Quarterly, Volume XXXIII, Issue 3, p 107, (2024) We present a novel approach to the age-old question of whether perfect
cuboids exist. Our approach consists of two new computer search algorithms,
arising from the analysis of "perfect plinths" reported by one of us recently,
that are much more efficient than any prior algorithm of which we are aware.
Using this approach, we also (i) identify some new two-parameter families of
edge cuboids, and (ii) show that large proportions of aspect ratios of faces or
internal rectangles cannot be present in a perfect cuboid, a property that was
previously reported only for faces with the aspect ratio 4:3. |
| Author | de Grey, Aubrey Gibbs, Philip Helm, Louie |
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| BackLink | https://doi.org/10.48550/arXiv.2401.06784$$DView paper in arXiv |
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| Snippet | Geombinatorics Quarterly, Volume XXXIII, Issue 3, p 107, (2024) We present a novel approach to the age-old question of whether perfect
cuboids exist. Our... |
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| Title | Novel required properties of, and efficient algorithms to seek, perfect cuboids |
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