改进镶边法构造任意奇阶同心幻方  

Construction of Arbitrary Odd Concentric Magic Square Using Improved Edging Method

作　　者：邓湘平[1] 

机构地区：[1]安徽大学化学化工学院,安徽合肥230039

出　　处：《海南大学学报（自然科学版）》2013年第3期199-204,210,共7页Natural Science Journal of Hainan University

摘　　要：首先引入了双关联等差数列的概念,借此提出了一个构造n阶幻方的充分条件,然后将奇阶幻方分为n=4m-1阶与n=4m+1(m=1,2,…,m∈N)阶两类,介绍了一种改进的镶边法,分别构造两类奇阶幻方,并给出了严格的证明.此构造法简单易行,灵活多变,所构造出的幻方具有独特的性质.In the report,the concept of the double associated arithmetic progression was introduced,a sufficient condition of constructing n order magic square was put forward,and the odd magic square was divided into two types：n =4m-1 and n =4m ＋ 1 （m =1,2,…,m ∈ N） order magic squares.A new improved edging method was used to construct two kinds of odd magic squares,and the mathematically strick proof was given.The construction method was simple and flexible.The unique properties were present in the constructed magic squares.

关 键 词：幻方 同心幻方 镶边法 双关联等差数列 十字旋转 

分 类 号：O157[理学—数学]