Dudeney's Dissection is Optimal
Erik D. Demaine, Tonan Kamata, Ryuhei Uehara
1907年,亨利·欧内斯特·杜德尼(Henry Ernest Dudeney)提出了一个难题:“将任何等边三角形......剪成尽可能少的碎片,这些碎片将拼合在一起并形成一个完美的正方形”(没有重叠,通过翻译和旋转)。 四个星期后,杜德尼展示了一个美丽的四件套解决方案,今天仍然是最著名的解剖例子。 在本文(一个多世纪后)中,我们终于解决了杜德尼的难题,通过证明等边三角形和正方形没有共同的剖析,有三个或更少的多边形。 我们将问题归结为分析离散图形结构,这些结构代表了形成每个多边形的碎片的边缘和顶点之间的对应关系。
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 wi...