8n阶完美富兰克林幻方的构造  

Making the 8 nth Order Perfect Franklin Magic Square

作　　者：徐向东[1] XU Xiang-dong(Wulanchabu Vocational College,Wulanchabu 012000,China)

机构地区：[1]乌兰察布职业学院,内蒙古乌兰察布012000

出　　处：《数学的实践与认识》2021年第10期308-315,共8页Mathematics in Practice and Theory

摘　　要：构造m=8n(n为正整数)阶完美富兰克林幻方,既有富兰克林幻方的弯曲对角线之和等于幻和L=m/2(m^(2)+1)的性质,又有两条对角线与所有泛对角线之和都等于幻和L的性质,是正规的完美幻方.使用一种新的构造方法,首先构造三个4阶完美方阵(全对角线方阵),即方阵的每行、每列与每条对角线同每条泛对角线各数之和都等于定值,然后建立通用矩阵公式构造8n阶完美富兰克林幻方.The m=8 n th(n is a positive integer)order perfect Franklin magic square constructed not only has the property that the sum of the bent diagonals of Franklin magic square is equal to the sum of magic sum L=m/2(m^(2)+1),but also has the property that the sum of two diagonals and all the pan diagonals is equal to the sum of magic sum L,which is the normal perfect Franklin magic square.A new method is used to construct three4 th-order perfect square matrices(full diagonal square matrices),of which rows,columns and the two main diagonals and pan diagonals have the same sum,and then the general matrix formula is established to construct 8 n th order perfect Franklin magic square.

关 键 词：富兰克林幻方 弯曲对角线幻方 完美幻方 完美富兰克林幻方 矩阵公式 

分 类 号：O151.2[理学—数学]