构造奇数阶幻方的杨辉口诀法

Yang Hui’s Formula Method for Constructing Magic Squares of Odd Order

摘要: 幻方在中国起源很早，最初是与河图与洛书相关联，后来古人称为九宫算或纵横图，它是最早发现的著名组合算题。在杨辉口诀法的基础上，通过对构造出的具体的奇数阶幻方的构造规律进行探寻，结合幻方矩阵化的思路及分块矩阵这个工具给出奇数阶幻方构造的通法，并且将杨辉口诀法进行推广应用于全体奇数阶幻方的构造上。

Abstract: Magic square has a very early origin in China. It was originally associated with river diagrams and Luoshu, and later it was called Jiugong calculation or vertical and horizontal diagram in ancient people. It is the earliest discovery of the famous combinatorial problem. On the basis of Yang Hui Formula method, this paper explores the construction law of odd order magic squares, combines the idea of magic square matrix and the tool of block matrix to give the general method of the con-struction of odd order magic squares, and generalizes Yang Hui Formula method to the construction of all odd order magic squares.