In mathematics, the Rubik's Cube contains the richest philosophical thoughts. The Book of Changes is a philosophical work, which has influenced almost all philosophical thoughts at home and abroad. However, scholars of Yi-ology found through various studies that Yi-ology originated from Hutu Luoshu, which is a third-order Rubik's Cube. The layout law and construction principle of the Rubik's Cube include the living structure of all things in the world, which is a mathematical model to explain the emergence and development of the universe. My essays "The Changing Thoughts of the Fourth-order Perfect Magic Square" and "The Fifth-order Magic Square and the Easy Number System" are further discussions on the philosophical thoughts contained in the higher-order magic square. Interested readers can refer to Zhouyi ResearchNo. 1999,No. 1, No.2000?
Second, the Rubik's Cube is applied to art design.
Magic square is widely used in art design. Bratton, a western architect, found that the symmetry of the magic square is quite rich. It uses the Rubik's cube to form many beautiful patterns. He called the square line in the pattern "Moline" and applied it to the design of light industrial products and cover packaging. The famous German printmaker A. Duller's work Melancholy is famous all over the world because of a Rubik's cube that can indicate the production time. The harmonious combination of artistic beauty and rational beauty is common. On the map of "Moline", Japanese Rubik's Cube expert Fang Yue has also done a lot of work. Ji Guangzhong, a teacher from Anyang, Henan Province, has drawn various magical maps and dedicated them to the Central Academy of Arts and Crafts. Beijing Ding Baoxun published 17 "Magic Diagram" in the Rubik's Cube Album, all of which are very beautiful. The mathematical layout in the Rubik's Cube is very symmetrical, balanced and varied. Therefore, if the numbers are connected in sequence, a strange "Rubik's cube array structure diagram" can be formed, and a very beautiful artistic pattern can be obtained after color processing. This pattern shows a variety of symmetrical beauty, but also has the rational law of Rubik's cube principle, so it is intriguing and can be called an axe.
Third, the aesthetic value of the Rubik's Cube.
Mathematics is beautiful, and the Rubik's Cube is even more beautiful. Rubik's cube is a system in which mathematics is arranged according to a law. Every Rubik's cube is not only an intellectual achievement, but also an artistic masterpiece. Generation has the characteristics of uniformity, balance, symmetry and harmony, shines with mathematical beauty and has high aesthetic value. In mathematical aesthetics, the aesthetic value of Rubik's cube has been pushed to the peak. Because all the contents in mathematics are closely related to numbers, the beautiful structure of the Rubik's Cube can penetrate all kinds of mathematical knowledge, show a variety of fun, and let us know many mysteries of mathematical knowledge in the appreciation of the Rubik's Cube. ?
Fourth, the intelligence development function of the Rubik's Cube. Rubik's cube is simple and easy to use, and will soon arouse young people's discussion interest. It can be said that the Rubik's Cube has played a very important role in intellectual development. Digging into the history of Chinese mathematics, we will find that interesting mathematics, calculation tools and board games are all internally related to the Rubik's Cube. In the history of algorithms, there are nine palace calculations, followed by Taiyi calculations, abacus calculations and electronic computers. In the history of game development, Jiugong was the first to be rearranged, followed by chess, Go and Huarong Road. Go chessboard is a 19-order square, and elephant chessboard is an 8-order square (its general palace is a 3-order square), and their moving principles are all related to the layout principle of the Rubik's cube. The computer game "Mining" is closely related to Nine palace map. ?
In recent years, researchers of China Rubik's Cube have invented many intellectual development games by applying the Rubik's Cube principle. Liu Zhixiong, Liaoning, designed a double-sided Rubik's Cube with a set of pictures and won the bronze prize; Anhui Wang Zhonghan designed an interesting Rubik's cube chess; Jiang, Hunan, designed Rubik's cube series digital game machines; Moreover, the author has successfully designed "Jiugong Miaoqi", which has nine functions and more than 20 game modes, and is an excellent garden for primary school students' mathematical operation training.
Fifth, the influence of Rubik's cube in mathematics teaching.
Rubik's cube in mathematics teaching has the functions of improving students' interest in learning, beautifying teaching materials and inspiring students' thinking. The various numbers in the magic square link all the contents in the mathematics textbook, such as equation magic square, radical magic square, fractional magic square, black hole number magic square, product magic square, difference magic square, square magic square and so on. Can be used in mathematics teaching to make mathematics content attractive. Graph 1 is a perfect magic square of order five. When a student learns the addition and subtraction of rational numbers and gives this number to the students for discussion, the students will carry out various learning activities with great interest. They will find that the sum of five numbers in the form of "ten, one, x and/"is all 0, and the sum of six numbers with "△" in figure 65438 must be. The magic square is an important content in the Olympic mathematics book. ?
Sixth, the inspiration of Rubik's Cube to science.
River map can be regarded as a second-order magic square model, and Luo Shu is a third-order magic square. Because of their wide spread, they have given people a lot of scientific enlightenment since ancient times. For example, in Einstein's theory of relativity, 1 1 formula is used to calculate the relative increase and decrease of time and space, and the Heluo number is very enlightening to him. Jiao Weifang, a Chinese-American scholar, has written Luo Shu Matrix, Luo Shu Ji Shu and Luo Shu Space, which promoted the development of mathematics. Fu Xiru, Henan Province used Luo Shu to study Goldbach's conjecture. We know that computers are based on automatic control theory. The inventor of American automatic control theory has made a series of control theories by studying China's "three-three maze diagram" (the line diagram of the third-order magic square). As can be seen from the data here, computers that are now popular all over the world have actually moved towards the Rubik's cube field. Rubik's cube has a natural property, although it is a numerical relationship, it is often abstract and general. When people think repeatedly, it may inspire a scientific theory and promote its development. In the traditional culture of China, we can see a lot of information about the application of Luo Shu in military, Chinese medicine, astronomy, meteorology, qigong and other fields, which shows that the close relationship between Rubik's Cube and various disciplines can not be ignored.
Seven, the Rubik's Cube is applied to science and technology.
The Rubik's Cube has been applied to the position analysis and combination analysis of "Road Building", "Absolute Curve" and "Seven Bridges". The Rubik's Cube leads to Laplace's guiding coefficient, Gauss theorem, Gerry theorem and Henri Storck theorem, and also leads to the electronic equations of Posen and Brutin. The Rubik's Cube also led to Sang Nan's automatic control theory, which led to the birth of electronic computers. Computers have three sources, binary (gossip), abacus and Rubik's cube. Electronic science has regarded the arrangement of magic squares as an ideal figure of electronic circuit networks. We can see from "Yi Shuo" written by Li Kaixuan, Taiwan Province Province that the first lesson for pilots in Taiwan Province Province to learn aircraft knowledge from Japanese is the knowledge of Rubik's Cube, because the construction principle of Rubik's Cube is closely related to the electronic circuit setup on the plane. Wu Longsheng, an expert in electrical engineering in Taiwan Province Province, invented the 64th-order square array instrument, which can be used in computers, measuring instruments, communication exchange instruments and control systems of water, electricity, fire and aviation, and has obtained a patent. For floating buildings on the sea, the first problem to be solved is to divide the building surface into square grids, and the determination of the building weight of each grid needs to be arranged as skillfully as the construction of a Rubik's cube, because as long as the weight of all lines and directions is balanced everywhere, it will not tilt. Mr. Tian Jian, a member of the Shaanxi Provincial Political Consultative Conference, has written a book and is applying the Rubik's Cube to study the theory of traditional Chinese medicine. He studied the digital characteristics of human etiology and the configuration of traditional Chinese medicine from the digital structure of the Rubik's Cube. His research work has attracted the attention of many medical scholars. The author applied the structure principle of the 10th Rubik's Cube to study the TCM theory of "505 Shen Gong Yuan Qi Bag" and achieved some results. Liu Jixi of Sichuan once designed Rubik's cube cultural products for toy factories, handkerchief factories, ball factories, umbrella factories and porcelain factories, and Xu Zhongyi of Jiangsu has designed Rubik's cube carpets. Beijing Gao Xuefeng owns many patents of "Rubik's Cube Cloth" and "Magic Array Therapy".
Eight, the role of the Rubik's Cube in cutting-edge science.
Here, I'd like to introduce the research results of Professor Qi, vice president and doctoral supervisor of north china university of technology. In his book Fractal and Its Computer Generation, there is a section "Kroneck Multiplication and Magic Square of Matrix", which discusses that the magic square has gradually developed its application from being only considered as a "strange phenomenon". If M-order magic square A and N-order magic square B are taken as matrices, then Kronecker product A? B is also a Rubik's cube. If m×n squares are set on the computer screen, the gray level of each square corresponds to the element value of m×n matrix A in turn, and the squares corresponding to aij are divided into P×q small squares at a time, and colored according to the value of aij*B, and so on. It is conceivable that the infinite nested structure obtained from the Rubik's Cube has self-similarity (external or internal) and can be regarded as a holographic corresponding structure. Because magic square is a special numerical matrix, Professor Qi found that Bezier -Bernstein surface generated by using magic square as the data matrix of control network has the property of one-way integral invariance, while other well-known approximation methods, such as B-spline interpolation or polishing, Lagrange interpolation, etc. , does not have this property. ?
The article "Digital Image Transformation and Information Hiding and Camouflage Technology" co-authored by Professor Qi and his doctoral students was published in China chinese journal of computers. This paper puts forward the technology of "image scrambling transformation according to magic square", which can scramble the images that need to be kept secret and then restore them according to magic square principle. This scrambling transformation can be performed many times. The author thinks that the classification, counting, construction program and transformation of magic square can be used in information hiding technology, and its application prospect will be very broad. ?
The author recently looked at the computer network system. There are five kinds of network topologies, each of which has its own advantages and disadvantages. But when we think about the structure of the fifth-order perfect magic square, five kinds of network structures can be integrated into one, which may become the most perfect network structure, a bit like the "five-element system" in our human body (TCM terminology). Shandong Wu Shuo's new theory of α (q, a) is very close to the basic principle of computer, and this theory derived from magic square will definitely find its application prospect in computer. Gansu Huang applied binary theory to study magic square. It breaks down the Rubik's Cube into several pieces, all of which are black and white, and they are in harmony and balance. These black and white blocks can definitely be used in computer technology. I hope everyone will study and develop. ?
With the further development of electronic computer, Rubik's Cube has been widely used in ergonomics, graph theory, game theory, experimental design, arts and crafts, electronic circuit principle, position analysis and so on. We can say that the Rubik's Cube has made great contributions to human civilization in ancient times, and it will also have broad application prospects in the information age today.