应用宏微控制法可以构造任何奇阶幻方；
本文首次给出了一个正规的16阶三次幻方。
In this paper, a normal 16th order trimagic square is published for the first time.
本文提出一种通过计算构作任意阶幻方的新方法。
A new method of constructing magic squares of any order has been put forward.
用时序控制器控制幻方光屏，可获得优美的动态图案。
With a magic square panel controlled by a sequence controller, wonderful dynamic patterns can be displayed.
本篇文章考虑了特殊四阶幻方的变换群及幻方分类的问题。
In this paper, the transformation groups of special magic squares of order 4 and the classification of magic squares are considered.
他附加条件，就对自己的价值有多少变数带来的创作他的幻方。
He imposed conditions on the value of his number variables to bring about the creation of his magic square.
并在此基础上给出了一种构作幻方的简便方法——方阵定位法。
On the basis of this method, a simple and convenient way of constructing magic squares the method of Locating Element by square Matrixes has been given.
对构造奇数阶幻方的菱形法进行了改进，并对改进方法进行证明。
This article improves the lozenge method to structure odd magic square and proves its improvement.
并在此基础上给出了一种构作幻方的简便方法——方阵定位法。
On the basis of this method, a simple and convenient way of constructing magic squares the method of Locating Element by square ma...
幻方变换加密数字图像，在某些迭代次数时会泄露原图像的信息。
Using the magic generating algorithms, some image information will be revealed in a digital image encrypted with magic transformation during the transforming process.
本文得出了一类单偶阶非等比数列乘幻方的构造法并用微机实现它。
In this paper, a constructive method for a kind of single even order magic squares generated by non geometrical sequences is obtained and realized on computer.
从十七世纪开始，人们对幻方的构造与性质展开比较严肃的数学思考。
People started to do some mathematical analysis on the structure and the character of magic square from seventeen century.
在4n阶幻方构造研究的基础上，一种4n阶幻立方构造方法被发现。
On the basis of the study on magic squares of order 4n, a method of constructing magic cubes of order 4n is discovered.
同时，利用矩阵加法构造幻方的方法，并且对它们进行程序设计，付诸实践。
At the same time, it shows that matrix addition is used to arrange magic square.
相比单纯使用幻方变换的加密方法，新方法有双重因素控制，有更高的安全性。
Comparing with the encryption method only using magic transformation, the new method has two controlling factors and is more secure.
接着利用变换群将特殊四阶幻方进一步分成了不同形式的9类，辅助于计算机程序可以搜索到具体结果。
Then we divide the special magic squares into different 9 classes under the action of given transformation groups. By making use of the computer programmer, the precise data can be searched.
通过研究特殊四阶幻方的变换，结合对称群中的置换元素相互作用生成的轮换关系，给出了192阶和384阶变换群。
We will manifest the existence of the transformation groups of order 192 and 384 by studying the transformations and rotation relations.
给出了单偶数阶和双偶数阶非等比数列乘幻方的构造方法，把乘幻方的研究从等比数列推广到了非等比数列；探讨了以任给自然数N为偶阶乘幻方值构造非等比数列乘幻方。
It initia1ly probes whether any natural number N can be used as a mumerical value of even order multiplier magic square to construct a multiplier magic square of non-geometric progression.
给出了单偶数阶和双偶数阶非等比数列乘幻方的构造方法，把乘幻方的研究从等比数列推广到了非等比数列；探讨了以任给自然数N为偶阶乘幻方值构造非等比数列乘幻方。
It initia1ly probes whether any natural number N can be used as a mumerical value of even order multiplier magic square to construct a multiplier magic square of non-geometric progression.
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