Trisecting a Rectangle
Trisecting a Rectangle
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DOI：
10.1016/0097-3165(94)90049-3
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发表时间：
1994-04
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影响因子：
--
通讯作者：
S. Maltby
中科院分区：
文献类型：
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作者：
S. Maltby
《关键数学》（Crux Mathematicorum）杂志上的第875题是要判断一个正方形能否被分割成三个相等但非矩形的部分。在1991年9月的那期杂志上，刊登了一份底片上的解决方案。本文将这一结果推广到更一般的问题，即一个矩形能否被分割成三个全等的非矩形块。这也推广了Stewart和Wormstein关于不存在3阶多项式的结论。如果一个矩形被分割成三个相等的部分，那么这些部分本身一定是矩形。此外，解剖必须采用图1所示的形式之一，第二种形式只有在矩形的长度和宽度比为3:2时才有可能。
Problem 875 in the problem-solving magazine Crux Mathematicorum was to decide whether or not a square could be dissected into three congruent but non-rectangular pieces. In the September 1991 issue a solution in the negative was published [1]. This paper extends that result to the more general problem of whether a rectangle can be dissected into three congruent non-rectangular pieces. This also generalizes the result of Stewart and Wormstein that there is no polyomino of order 3 [2].THEOREM. If a rectangle is dissected into three congruent pieces then those pieces must themselves be rectangles. Further, the dissection must be in one of the forms shown in Fig. 1, the second being possible only when the length and width of the rectangle have a ratio of 3: 2.