Dudeney's Dissection is Optimal
2024/12/05 by Erik D. Demaine, Tonan Kamata, Demaine, Erik D. +3 · 9 voices
#cs.CG #cs.DM #math.GT
paper · pdf · doi:10.48550/arxiv.2412.03865
Abstract
In 1907, Henry Ernest Dudeney posed a puzzle: ``cut any equilateral triangle … 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.
Discussions
- In 1907, Henry Dudeney showed that you could dissect a square into 4 pieces that can be rearranged to form an equilateral triangle. In 2024, Erik D. Demaine, Tonan Kamata and Ryuhei Uehara proved tha [bsky, 27 points, 1 comments]
- J'ai fait une courte vidéo récemment pour annoncer la résolution, mais sans parler du tout de la preuve. L'idée pour cet aprem, ce sera de lire ensemble le papier de Demaine, Kamata et Uehara. Il est [bsky, 7 points, 0 comments]
- 정삼각형을 분할하여 정사각형을 만드는 듀드니 퍼즐의 네 조각짜리 해법이 최적임이 증명되었다고. Dudeney's Dissection is Optimal Erik D. Demaine, Tonan Kamata, Ryuhei Uehara arxiv.org/abs/2412.03865 [bsky, 2 points, 0 comments]
- "Dudeney's Dissection is Optimal Erik D. Demaine, Tonan Kamata, Ryuhei Uehara - arXiv" 5 Dec 2024 arxiv.org/abs/2412.03865 [bsky, 0 points, 1 comments]
- これだよね。全然読めてないんだけど（パスの段階でお手上げ） arxiv.org/abs/2412.03865 [bsky, 0 points, 0 comments]
- doi.org/10.48550/arX... [bsky, 0 points, 0 comments]
- arxiv.org/abs/2412.03865 [bsky, 0 points, 0 comments]
- arxiv.org/abs/2412.03865 by Erik D. Demaine (@mitofficial.bsky.social), Tonan Kamata & Ryuhei (Japan Advanced Institute of Science and Technology) [bsky, 0 points, 0 comments]
- From December, but I missed it at the time: Dudeney's Dissection is Optimal https://arxiv.org/abs/2412.03865 [bsky, 0 points, 0 comments]
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