论文标题
亚当·亚当迪·科尚斯基（Adam AdamandyKochański）减法的魔法平方
Magic squares of subtraction of Adam Adamandy Kochański
论文作者
论文摘要
魔术广场建造的问题占据了17世纪的许多数学家。波兰耶稣会士和多律师亚当迪·科尚斯基也研究了这一主题，并在1686年发表了一篇论文，以“考虑因素”为“ Quaedam Quaedam Circa Quadrata et cubos Magicos”。在那篇论文中，他提出了一种新型的魔术方形，在每个行，列和对角线中，如果条目以减少顺序排序，则具有奇数指数的条目和偶数指数的条目之和之间的差异是恒定的。他称它们为\ emph {quadrata subractionis}，意思是减法的平方。他举了这样的订单4和5正方形的例子，并挑战了读者制作第6阶的平方的示例。我们讨论了他用来产生第5个正方形的可能方法，并表明它可以推广到任意奇数。我们还展示了如何构建双重的正方形。最后，我们展示了Kochański寻求的命令6正方形的示例，并讨论了减法正方形的枚举。
The problem of the construction of magic squares occupied many mathematicians of the 17th century. The Polish Jesuit and polymath Adam Adamandy Kochański studied this subject too, and in 1686 he published a paper in Acta Eruditorum titled "Considerationes quaedam circa Quadrata et Cubos Magicos". In that paper he proposed a novel type of magic square, where in every row, column and diagonal, if the entries are sorted in decreasing order, the difference between the sum of entries with odd indices and those with even indices is constant. He called them \emph{quadrata subtractionis}, meaning squares of subtraction. He gave examples of such squares of orders 4 and 5, and challenged readers to produce an example of square of order 6. We discuss the likely method which he used to produce squares of order 5, and show that it can be generalized to arbitrary odd orders. We also show how to construct doubly-even squares. At the end, we show an example of a square of order 6, sought by Kochański, and discuss the enumeration of squares of subtraction.
