Magic square

directory

Overview same word meaning different species entirely by magic square magic square of order n magic squares and magic squares of order n equal to the number of anti-magic squares and magic squares appreciate history programming construct third-order magic square dislocation supplementary angle method to generate the odd magic square Expand edit this section outlined by a number in a number composed of neatly arranged in a square, a rampant arbitrary figure, a vertical line and a few number of diagonals are equal, chart of this nature, known as the "magic

Luoshu, a magic square of order 3

side. "Chinese ancient times was called" Riverside "," Luo Shu ", also called" aspect graph. "JiuGongTu Luoshu contains Miracle Fighters The lineup of the road. JiuGongTu number from the I Ching, the "Book of Changes." magic square, also known aspect graph, cube, magic array, it is the science of crystallization and auspicious symbol, originated in ancient China Luo Shu - - JiuGongTu. century BC, the Western Han emperor when Boshidaide in his political etiquette book "The Big Day ceremony hall and articles" in there "two, nine, four, seven, five, three, six, one , eight, "the number of records Luoshu nine palaces. Luoshu been recognized as the originator of combinatorial mathematics, which is the great contribution of the Chinese nation is one of mankind while Luoshu its highly abstract connotation of ancient Chinese political ethics, mathematics, astronomy and meteorology, philosophy, medicine, religion, etc. have an important impact in the ancient legend, in the country and bringing peace also has a positive meaning! including Luo Shu magic square since ancient times, including in Asia, Europe, the Americas Many countries have been used as drive away evil mascot, this geographically widespread ancient totem should say is extremely rare. 1975 Shanghai People's Publishing House Books Dialectics of Nature "natural sciences Chronology" magic square for the a special recount: "the first century BC," Big Man "records, ancient Chinese symbol of good luck Hetu aspect graph, namely JiuGongTu count, is considered to be modern 'combinatorial mathematics' oldest discoveries. "The only attachment to the book illustrations! 2,500 years ago, Confucius in his study" I Ching "book" copula Upload "recorded:" The River plot, Los a book, then the saints. "Was first connected to the digital records with Luoshu 2300 years ago," Zi-day operation, "it said:" There are six days of very Wuchang, emperor Shun then treat the reverse is just as fierce. Nine Luo things, governance into Germany prepared, according to soil under supervision, the world wear it, we called Shang Huang. "Ming mathematician Cheng Dawei in" algorithm Tongzong "and has also issued a" Digital Ho Chao? Since its Hajime figure, the book almost? Fuxi was to draw the hexagram, Yu was to order the domains of the Holy was to open the thing, "sighs, to the effect that the number originated in ancient times the Yellow River map appears with the Lo appear Luoshu, Fuxi rely River drawing out gossip, according to Luo Shu Yu divided Kyushu and develop nine categories of world governance Dafa, according to their interpretation of the holy people of a variety of country and bringing peace good way of understanding human society and the natural world has also been deepened step by step. the number of books from the Luo Yu mutual restraint, balance and be inspired to develop a unified national legal system, making world is unified, attributed Dazhi, thinking this is the beginning of learning. Such activation scientific way of thinking has become a source of inspiration From the originator of the Luo Shu magic square in a few thousand years later, more full of vitality, is referred to as having eternal charm mathematical problems. thirteen century, the Chinese mathematician Yang Hui Song first in the world to carry out a systematic study on the magic square European fourteenth century also began work in this area. famous mathematician Fermat, Euler magic squares have been studied, and now, is a combination of mathematical magic square is still one of the topics of study, after generations of mathematicians and mathematics lovers together, magic square with its variants inherent nature of the various magical science is gradually revealed. Currently,Nike Mercurial Vapor Superfly Fourth Style CR 5 FG Exclusive Personal Soccer Cleats White Green Red, it has been in portfolio analysis, experimental design, graph theory, number theory, group, game theory, textiles, arts and crafts, programming, artificial intelligence and other fields are widely used in 1977, 4 magic square also serves as a special human language is U.S. Voyager 1, 2 spacecraft to carry into space, to the vast universe that may exist in the outer Star who convey information to human civilization and good wishes! Edit this paragraph with the word different meaning

jade magic square

magic square, jade. It is the belief of Muslims supporter thereof. Rectangular, with two ears can be tied Shengpei hang. Positive for the round convex, engraved in Arabic, the back box 4 lines of 16 cells, each cell fill an Arabic numeral. Has a certain mystique. [1] Edit this paragraph completely species entirely magic square magic square magic square represents a row, diagonal, and "break" the diagonal equal to the sum of the numbers. Multiplied by magic square magic square magic square represents one ranks number equal to the product of the diagonal. n-order and high-order magic square magic square magic square of order n is a former n ^ 2 (n-th power of 2) consisting of a natural number n square matrix whose rows, columns and diagonals contained Edit this paragraph n numbers and equal. Examples: (third-order magic square, magic, and is 15) 492357816 mandatory five third-order magic square intermediate magic square is higher, when the number of replacement components for the magic square 2,3 , ..., k th power, still satisfy those conditions magic square, called this magic square magic square is k times. Anti-anti-magic square magic square definition: in a number consisting of several rows of square, in any one transverse drawing, a vertical and diagonal lines are not equal the number of a few, of such a nature charts, known as the "anti-magic square." Anti-magic squares and magic squares are the biggest difference is that magic and different, are all magic and magic squares are the same, and all anti-magic square magic and are different. The so-called magic square magic and that any rows, columns and diagonals several numbers. As shown anti-magic square of order 3 Comparison

anti-magic square

figure digits of the external borders is magic and. Red is even, odd black. It can be said anti-magic square is a special kind of magic square. Anti-magic squares and magic can all be different, the same can also be part of. As shown against a variety of third-order magic square.

variety of anti-magic square

Edit this paragraph history of the magic square, also known as cube, square or hall square, which originated in China. Song mathematician Pascal called aspect graph. Magic square magic lies in a matter which route to take, and finally get the sum or product are identical. About two thousand years ago,Adidas Predator XII TF, the Western Han dynasty, spread Yu flood, the Yellow River jumped a horse of God, laden with a figure on horseback, called "river map"; another Lo river floats a turtle, Turtle on an auspicious pattern called "Luo Shu." They found that the pattern of each column, each row, and diagonal add up numbers and are the same, this is what we now call the magic square It was also observed that "Luo Shu" is the alien relic; while the "Riverside" is a description of the biological universe (including aliens) gene collation magic square is alien to the people of the earth self introduction addition a few years ago in Shanghai Pudong Lujiazui area dug up an era of Islam believers Yuan hanging jade hanging, hanging jade front reads: "no god, only Zhenzai, Mohammed, their messenger ", and jade hanging on the other side was a four magic square. concerning the origins of magic squares, China has" Riverside "and" Luo Shu "said. According to legend, in ancient times, Fuxi made the world, the state of governance in good order, moved heaven, so the Yellow jumped a vigorous, back, laden with a map, as a gift to him, this is the "river map" also the first magic square. Fuxi virtue of the "Riverside" and deduce gossip, and later a large Yu Zhihong water, it floats a big turtle in the Lo, it's back there are pictures and words, known as "Los books." "Luo Shu" by the drawing in a total black, white circle 45. Put these together represented a small circle and number, get nine. The nine numbers can be composed of a vertical and horizontal figure, people from the nine 3 Row 3 magic square called 3 magic square, in addition, there are four bands, five bands ... Later, after research, come in arbitrary order magic square of each row, each column, all the various numbers on the diagonal and the formula: S = n (n ^ 2 +1) / 2 where n is the order of the magic square , the required number of S. magic square first recorded in 500 BC Chinese Spring and Autumn Period "Big Man", which described China as early as 2500 years ago, people already know the magic square arrangement of law. In foreign countries, AD 130, the Greek Cypriot Weng first time brought the magic square. China not only has the right to the invention of the magic square, magic square and is carried out in-depth study of the country. 13th century mathematician Pascal has compiled a 3-10 magic square, documented in his 1275 book, "continued the ancient Abstract hall algorithm," a book. In Europe, until 1514, was a famous German painter Dürer draw out the full four magic square. In foreign countries, the twelfth century Arabic literature has documented six magic square, Chinese archaeologists have discovered in Xi'an in Arabic offering up five six magic square, in addition to these, the earliest history of fourth-order magic square is found in India, it is a totally magic square (mentioned later), and even earlier than China's Pascal's two hundred years, the Indians thought it was god's handwriting .1956 Xi'an unearthed an iron Chip panel of carved six magic square (ancient Arabic numerals) the thirteenth century, the Eastern Roman Empire fishes magic square generate interest, but did not achieve anything until the fifteenth century, lived in Constantinople magic cable Pula and only then China's aspect graph passed European, Europeans believe magic square can suppress demons, so put it as a talisman, but also called it "Magic Square." Europe's first magic square is a name in Germany painter Albrecht Dure's painting, above a fourth-order magic square, and this magic square is just below the two figures produced this painting's (1514), which is Europe's oldest magic square. Edit this paragraph At present China has made a lot of records magic square of World Records: first a magic square Experts Levin successfully constructed standard magic cube 10 order, the first one constructed five lowest-order magic square of order 729, and the number of square magic square of World Records, magic square Experts Su Mao very first one constitutes a successful 32-step perfect square magic squares, etc. to draw attention, arbitrary magic square construction method, arbitrary dimensional magic square construction method, any number of times Magic Squares method, have long found. no maximum Magic Square of the class world record for a variety of media coverage magic square in the world,Adidas AdiPure TF, many of them are false reports. maximum order does not exist unsolved magic square. Edit this paragraph magic square magic square appreciate China Website: [1 ] Chinese magic square blog: French high-order magic squares Website: [2] Japan multidimensional magic square Website: [3] Franklin's magic square: [4] nine-order square magic square: [5]

12 magic square

twelve bands perfect magic square (each 2 × 2 sub-matrix and 286): Edit this paragraph programming currently using a computer program, and any order can be solved magic square. (but limited number of digits by computer, in fact, only a limited range of arbitrary order), as calculated using Matlab magic square of order n, the command: A = magic (n). For some squares magic square, high-order magic square, using computer-aided calculation can also be quickly obtained. a magic square, a magic cube, a multi-dimensional magic square, or even all obtained using a simple formula. certain types of magic squares of squares, and even high times higher dimensional magic square, obtained from the formula can also be used in magic squares method for solving equations, China is a world leader in China's high-dimensional higher Levin magic square formula, magic square theory is fine. Wu Shuo Xin higher Magic side theory, the formula can also be used to solve. Edit this paragraph constructed in the "Legend of the Condor Heroes" in Guo Huang They were Qiuqian Ren Heilongtan catch, hide Yinggu hut. Yinggu out a question: fill in the numbers 1 to 9 to form three rows and three columns, requiring every row, column, and two diagonal and are equal. This question stumped Yinggu ten years, was suddenly Huang Rong answer out. 492357816 This is a simple planar magic square of order 3. Because intellectual magic squares and interesting games and toys are very magic square with related, such as Zhuofang Cao, we usually play hexahedral, has become a common problem when learning to program. Magic square known aspect graph, JiuGongTu, first recorded in ancient Chinese Luoshu. Said Yu flood when the big river near Luoyang, Henan Province emerged a turtle, back with a very strange pattern, the ancients considered an auspicious, indicating that the flood will be Yu Wang completely uniform. Later known as "Luo Shu" or "Riverside", also known as Luo map. Song mathematician Pascal, in his forward to the "continued the old pick odd algorithm" in the introduction to this approach: as long as the nine natural numbers in ascending oblique row in ascending order, and then, the next two numbers reversed, left, right two numbers are reversed; finally the middle four numbers to the outside of each elongation, magic squares appeared. (Excerpt from "fun math dictionary") is the most simple magic square magic square plane, as well as three-dimensional magic square, high-order magic squares and so on. For the three-dimensional magic square, the higher magic square mathematicians currently still studying many of the world is now only discuss planar magic square. Magic square of the plane structure, divided into three cases: N is an odd number, N is a multiple of 4, N is an even number other (4n +2 form) ⑴ N is odd, the simplest: ⑴ the 1 in the first row middle one; ⑵ starting from 2 until the number of n × n order for each store according to the following rules: the direction of 45 ° to walk, such as the right of every number stored in row number than the previous one less than the number of rows, number of columns plus one ⑶ If ranks beyond the scope of the matrix range, wraparound. For example one of the first row, the two should be placed on the next line, the same number of columns plus 1; ⑷ according to the above rules to determine if the position for several, or on a number of the first row and the first n columns, put down a number placed on a number below. ⑵ N is a multiple of four symmetrical element exchange. First, the numbers 1 to n × n top to bottom, left to right order of the matrix and then fill in all the 4 × 4 square sub-matrix of the two numbers on the diagonal position symmetrically about the center of the square exchange, namely a (i, j) and a (n +1- i, n +1- j) exchange, the number of all the other locations of the same. (Or the same diagonal, symmetric swapping can also be other locations) ⑶ N for other even when n is not a multiple of 4 when the even (ie 4n +2 form) is: First, the large square divided into four odd ( 2m +1 order) sub-matrix. According to the odd-order magic square of four sub-matrix corresponding to the decomposition of the assignment on the left subarray minimum (i), under the right sub-sub-sub-array (i + v), lower left subarray maximum (i +3 v), on the right sub- Array second largest (i +2 v) corresponding to the four sub-matrix element away from v, where v = n * n / 4 four sub-matrices arranged in ascending manner ① ③ ④ ② and corresponding switching elements: a (i , j) and a (i + u, j) to make the corresponding switch in the same column (j