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幻方是由1、2、…、m~2这m~2个自然数组成的m×m方阵,它的每一行、列以及主、副对角线上的各数之和都等于同一个数,即1/2(1+m~2)m。当m为奇(偶)数时,称此幻方是奇(偶)阶幻方。奇阶幻方与偶阶幻方在性质上有很大不同,中国古代数学家曾对此作过许多探讨。多年来人们曾作过种种努力,探索利用公式构造奇阶幻方的方法。本文给出一种新的表达式。一、作法步骤:设m=2n+1。 1.建立xOy直角坐标系,选取m~2个整点:
The magic square is an m×m square matrix consisting of 1, 2, ..., m~2, m~2 natural numbers. The sum of the numbers in each row, column, and main and subdiagonal lines is equal to the same. The number is 1/2 (1+m~2)m. When m is an odd (even) number, this magic square is called an odd (even) magic square. There is a big difference in the nature of odd-order magic squares and even-order magic squares. Ancient Chinese mathematicians have done a lot of research on this topic. Over the years, people have made various efforts to explore the use of formulas to construct odd-order magic squares. This article gives a new expression. First, practice steps: Let m=2n+1. 1. Create a xOy Cartesian coordinate system and select m~2 full points: