泛系方法论与幻方算法构造

本文论述系统方法论的精缩影模式及其对求解、建模、算法生成与理论建构的作用,用时用泛系方法提出并证明了:1.递归构造n阶幻方(n≥5)的方法;2.已知m阶幻方和n阶幻方(m,n≥3),求mn阶幻方的公式;3.已知m阶幻方(m≥3),构造2m阶幻方的方法。利用本文算法用计算机可以排出任何阶的幻方。另外,本文论述了幻方的科学研究意义与潜科学意义。

Pansystems Methodology and Algorithm Construction of Magic Squares

Some patterns of refined epitomes of pansystems methdology are revealed in this paper and the related roles of them in problem - solving, modeling, algorithm - generating and theoryconstructing are introduced. An important application of pansystems methodology is to give some methods of constructing the typical pansymmetries - magic squares: 1. a method of recursively constructing magic squares of order n(n>4);2. when magic squares of order m(m >2) and magic squares of order n(n>2)are given,a formula of obtaining magic squares of order mn;3. when magic squares of order m(m>2)are given,a method of obtaining magic squares of order 2m.