Dudeney's Dissection is Optimal
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911086337327104 |
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| author | Demaine, Erik D. Kamata, Tonan Uehara, Ryuhei |
| author_facet | Demaine, Erik D. Kamata, Tonan Uehara, Ryuhei |
| contents | In 1907, Henry Ernest Dudeney posed a puzzle: ``cut any equilateral triangle \dots\ into as few pieces as possible that will fit together and form a perfect square'' (without overlap, via translation and rotation).
Four weeks later, Dudeney demonstrated a beautiful four-piece solution, which today remains perhaps the most famous example of dissection.
In this paper (over a century later), we finally solve Dudeney's puzzle, by proving that the equilateral triangle and square have no common dissection with three or fewer polygonal pieces.
We reduce the problem to the analysis of discrete graph structures representing the correspondence between the edges and the vertices of the pieces forming each polygon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dudeney's Dissection is Optimal Demaine, Erik D. Kamata, Tonan Uehara, Ryuhei Computational Geometry Discrete Mathematics Geometric Topology In 1907, Henry Ernest Dudeney posed a puzzle: ``cut any equilateral triangle \dots\ into as few pieces as possible that will fit together and form a perfect square'' (without overlap, via translation and rotation). Four weeks later, Dudeney demonstrated a beautiful four-piece solution, which today remains perhaps the most famous example of dissection. In this paper (over a century later), we finally solve Dudeney's puzzle, by proving that the equilateral triangle and square have no common dissection with three or fewer polygonal pieces. We reduce the problem to the analysis of discrete graph structures representing the correspondence between the edges and the vertices of the pieces forming each polygon. |
| title | Dudeney's Dissection is Optimal |
| topic | Computational Geometry Discrete Mathematics Geometric Topology |
| url | https://arxiv.org/abs/2412.03865 |