阿达莫斯幻方数学原理破解及其应用可能性探讨
- 来源：新浪科技 作者：橘子 时间：2008-05-05 22:04:54
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学科：数学-其它
作者姓名：孟繁星
年级：高三
所在学校：天津市第一中学
阿达莫斯幻方是指将1～19的自然数填入右侧图形中，使横、斜各行数字之和均为38，这个构造由美国人阿达莫斯花费了47年时间于1957年提出，但没有该幻方的数学原理。据检索，本文为首次提出该幻方的数学原理。
我经过研究探索，通过推导公式、排列奇偶数分布图、虚拟填充、证明对称性以及并行关联运算等方法，发现了阿达莫斯幻方的数学原理和构成方法。
目前高阶幻方数字排列是采用大量计算机进行分布式并行运算才能解出的。采用我发现的数学原理和构成方法，将可以快捷地构造出4阶及更高阶的幻方。
该原理和构成方法可能的应用领域：密码技术、益智游戏、导弹防御系统、复合材料、图论“完美匹配”、建筑学，如大空间结构的屋顶、类似“鸟巢”建筑等。
A magic hexagon of order 3 is an arrangement of numbers in this diagram, in such a way that the numbers in each row, in all three directions, sum to the same magic constant 38. Mr. Adams came across the problem in 1910. He worked on the problem by trial and error and after 47 years arrived at the solution. Until now, there still hasn’t been a mathematical principle on issues discussing the construction of magic hxagons. This report is found to be the first to have put forward the mathematical principle of the order 3 magic hexagon.
In my approach, I used and created several methods, including deriving necessary formulae, finding possible distributions of odd & even numbers, virtual filling, proving symmetry and conjunctive parallel algorithm. And finally found some of the magic hexagon’s unique properties, and the way of constructing the order 3 magic hexagon.
Up to now, solutions of magic hexagons of order 4 to 7 have been found by Zahray Arsen, using distributed and parallel computing. If my theories of the n=3 magic hexagon can be extended to those of order ≥ 4, there might be a possibility of constructing magic hexagons of higher dimensions more easily.
The theories and constructing method of the magic hexagon can be used in some fields of application, such as password system, cryptography, “perfect match” problem of graph theory, missile defense system, compound material and architecture, i.e. large-scale roof structure, which is similar to the “bird’s nest” structure.
Mathematical Paper: Researches Into The Mathematical Principles And Construction Of The Order 3 Magic Hexagon With Its Possible Applications
Category: Mathematical SciencesSubcategory: Other
Author: Fanxing Meng
Year 12
Tianjin No.1 High School
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