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# Topic: Magic square

###### In the News (Sat 17 Aug 19)

 magic square - Encyclopedia.com magic square a square divided into parts with letters or numbers inscribed therein that, whether combined vertically, horizontally, or diagonally, form the same sum or the same word. Magic squares have been found in such widely divergent cultures as ancient China, Egypt, and India, as well as W Europe. The association between Magic Johnson's HIV serostatus disclosure and condom use in at-risk respondents. www.encyclopedia.com /doc/1E1-magicsqu.html   (1006 words)

 Magic square Summary In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum. In the magic square of order four, the numbers in the four central squares and one square at each corner are retained in the same place and the others are interchanged with their diametrically opposite numbers. www.bookrags.com /Magic_square   (2733 words)

 The Magic Square Record A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum. Interesting records for multi-magic squares (not only the sum of the numbers but also the sum of their squares, cubes, etc. must be the same) can be found at www.multimagie.com. It is allowed to compose the magic square from many sheets of paper, but they MUST lay together to form one scheme of numbers. www.recordholders.org /en/records/magic.html   (288 words)

 Affine Magic Squares   (Site not responding. Last check: 2007-10-07) The rows, columns, diagonals, and other "magic" features of Dürer's square can be seen to be affine subspaces, naturally sorted into groups of four parallels. If a 4x4 magic square is magic on the parallel family of subspaces that includes the diagonals, then it is called "quasi-pandiagonal." The quasi-pandiagonal magic squares are a natural set to study using the techniques of affine subspaces. Looking at the Dürer square, we see that each base-p digit is determined by an affine functions, which is non-constant on the first row, the first column, and the main diagonal. www.monmouth.com /~chenrich/AffineMagicSquares.html   (1129 words)

 Count On - Kaleidoscope   (Site not responding. Last check: 2007-10-07) Magic squares were thought to have protective powers against illness and evil spirits. The numbers in a magic square sould be the same as the number of cells (for examples in a square of 3 x 3 the numbers are 1 - 9); and they are placed so that each row, column and the two main diagonals all sum to the same total. A magic square of order 4 has 16 cells (4 x 4), a magic square of the order 9 has 81 cells (9 x 9) and so on. www.mathsyear2000.org /magnet/kaleidoscope2/MagicSquare/index.html   (402 words)

 Magic Square magic square is a square array of numbers with the property that the sum of each row, each column, and each diagonal is the same. Magic squares have been found in ancient writings from many parts of the world, and in some cultures they were thought to possess magical or supernatural powers. A magic square remains a magic square if the same number is added to each element or if each element is multiplied by the same number. www.occultopedia.com /m/magic_square.htm   (823 words)

 Grogono Magic Squares Home Page A Magic square is intriguing; its complexity challenges the mind. This is particularly true when the Magic Carpet approach is used to analyze or construct a magic square, e.g., to construct an order four magic square, four magic carpets would be required using: 8 and 0; 4 and 0; 2 and 0; and 1 and 0. My fascination with magic squares grew from experimental attempts to count the total number of possible squares when squares which, apparently different, were really identical when appropriately reflected or rotated. www.grogono.com /magic   (818 words)

 Magic Square Models Any pandiagonal magic square may be considered as being on the surface of a torus in stead of a plane. In effect, the magic square is on the surface of a torus instead of a plane. Magic sum is 42 on all the 9 rows, 9 columns, 9 pillars and 4 triagonals. www.geocities.com /~harveyh/ms_models.htm   (1198 words)

 Math Forum: Allan Adler - What is a Magic Square? A magic square is an arrangement of the numbers from 1 to n^2 (n-squared) in an nxn matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. The 4x4 Dürer magic square (or, what is essentially the same, the 4x4 magic square I use) has many interesting special properties that are not shared by magic squares in general. From (1) and (2), it follows that the left half of the square has the same sum as the right half and that this is one-half the sum of all of the numbers in the square. www.mathforum.org /alejandre/magic.square/adler/adler.whatsquare.html   (523 words)

 Magic Squares Magic squares have been studied for at least three thousand years, the earliest recorded appearance dating to about 2200 BC, in China. Because the concept of a magic square is so easily understood, magic squares have been particularly attractive to puzzlers and amateur mathematicians. When this upward-right movement would result in a location outside the boundaries of the square, we place the new number at the opposite end of the row or column that would contain the new number, if the rows and columns were not bounded. www.jcu.edu /math/vignettes/magicsquares.htm   (742 words)

 magic square operations The dimension of each magic square in the stack is shown in the windows below the input window. Addition of magic squares does not result in another magic square, so they cannot be added. A magic square is composite if it is the product of two strictly smaller magic squares. home.att.net /~srschmitt/script_magic_squares_ops.html   (410 words)

 A very, very Magic Square Then entries of the square are the numbers 1,2,...,625=25x25. If the square is divided up in 25 5x5 squares, then all those little squares are magic too: they all have row, column and diagonal sums equal 1565=5x(1+625)/2. If one squares all entries in in the square, the square remains magic: all row,column and diagonal sums are equal to 3263025. www.math.lsa.umich.edu /~hderksen/magic.html   (114 words)

 the magic square The square was magic because, no matter which way the Emperor added up its lines, the numbers came to the same total. Numbers of a magic square are complements if their sum is the same as the sum of the smallest and largest numbers of a magic square. Any number may be either added or multiplied to every number of a magic square and it will remain a magic square. library.thinkquest.org /25672/themagic.htm   (248 words)

 allmath.com - math site for kids! Home of flashcards, math biographies and Ask The Experts Magic squares have been a fascinating topic in mathematics for centuries. They are formed by filling in all the squares with the numbers starting from one so that the sum of all row, columns, and diagonals is the same. In the easy level, you are given the numbers beginning from one and must create a magic square. www.allmath.com /magicsquare.php   (675 words)

 Create a Magic Square for any number in Excel If you are about to write a number in a yellow or red square, you would have to write the number in the cell that is diagonally opposite from that square. If you added one to every cell, the magic square would total 38, because all 4 cells would be incremented by 1. The key to creating a magic square that adds up to any number is to vary the starting number. www.mrexcel.com /tip069.shtml   (1186 words)

 Magic Square of Squares Report concerning magic square of squares (3x3) Jan/99 =============================================== In "Scientific American" VIII.98 Martin Gardner in his quarter century review mentioned the above problem : rows and columns to have the same magic some of distinct squares as well as both the diagonals. On the other hand both solutions to the relaxed problem I succeeded to find have a square as a magic sum : there is foundation to suppose, not only by accident. By the way if we tile the plane with one of these patterns every square of (3x3), which is cut out anywhere, has the (relaxed) magic property. www.private.org.il /magic_square.html   (469 words)

 Magic Square / Atomic Art Magic Squares are ancient boxes of numbers whose sums of rows, columns and diagonals all add up to the same sum. Even though the Magic Square appears to be a random box of numbers, when we analyse it or x-ray it or pull it apart, we discover this hidden or inherent patterning inside. When we work with the Magic Square of the Sun, which is the 6x6, we are dealing with all the numbers from 1 to 36, all columns and rows and diagonals add up to 111, and therefore the sum of all numbers is 666. www.jainmathemagics.com /page/1   (5692 words)

 PlanetMath: Franklin magic square   (Site not responding. Last check: 2007-10-07) Furthermore, half any row or column (positions 1 to 4 or 5 to 8) equals half the magic constant. Some other 8 by 8 magic squares with these properties are also called Franklin magic squares. This is version 1 of Franklin magic square, born on 2006-11-16. planetmath.org /encyclopedia/FranklinMagicSquare.html   (131 words)

 Magic Squares Program Magic squares are arrays of numbers where the rows, columns and the diagonals add up to the same number, (called the square's constant). The main point of the project was to write a program that could generate magic squares of all sizes, but my research failed to uncover a workable algorith for "Single Even" sizes. The book I had showed filling the base square diagonals with the numbers from 1 to "size" and then filling in the remaining cells with the numbers not used. www.wctatel.net /web/blevad/magic_squares.html   (1167 words)

 Magic Square Unlike the 3x3 square there is not just one conclusion for the distribution of the numbers 1 to 16 in a 4x4 square. The Latin square, which is formed by 1,2, and 3 and has different numbers in every row and column, is an example of a semi-magic square. A square is panmagic, if it is magic and if the numbers have the same sum in the corners, in the centre and on the edges. www.mathematische-basteleien.de /magsquare.htm   (919 words)

 magic squares at Math Cats: fun, easy, and interactive!   (Site not responding. Last check: 2007-10-07) In magic squares, each row and each column and each diagonal adds up to the same number. This special magic square adds up to the same number in all of these ways. The most magic thing of all is that you can see the year "1514" in the middle of the bottom row. www.mathcats.com /explore/puzzles/magicsquare.html   (139 words)

 Magic Squares   (Site not responding. Last check: 2007-10-07) This is a magic square of order 3 (three numbers to the side of the square). Briefly, the square of 4 is the square of Jupiter. the corresponding magic square, and painted in the corresponding colour. www.ismaili.net /mirrors/Ikhwan_08/magic_squares.html   (7223 words)

 [No title] This page is dedicated to magic sequences, to form regular magic squares. The magicness of the square is automatic by the above mentioned theory. According to this distinction the last two prime number magic square are of type 2 while all the others are of type 1. home.wanadoo.nl /aaledewinkel/Gen_Magic/MagicSequences.html   (488 words)

 Magic Squares The idea of the magic square was transmitted to the Arabs from the Chinese, probably through India, in the eighth century and is discussed by Thabit ibn Qurra (known for his formula for amicable numbers) in the early ninth. A list of squares of all orders from 3 to 9 are displayed in the Encyclopaedia, (the Rasa`il), compiled about 990 by a group of Arabic scholars known as the "brethren of purity" (the Ikhwan al- safa), (see [11], Vol. The magic square at the right comes from pg 104 of The Man Who Counted, a fable about mathematics by Malba Tahan (which I belive is the pseudonym of Júlio César de Mello, a Brazilian Mathematics Professor). www.pballew.net /magsquar.html   (917 words)

 Muse: Magic Squares The magic square is hanging on the wall to the upper right. Astrologers in Dürer's time associated different types of magic squares with the planets, which, in turn, were thought to influence health. He's famous among number fanatics for an amazing eight-by-eight magic square containing the numbers from 1 to 64. www.sciencenewsforkids.org /pages/puzzlezone/muse/muse1103.asp   (470 words)

 Math Trek: Magic Square Physics, Science News Online, July 1, 2006   (Site not responding. Last check: 2007-10-07) A magic square is a square matrix drawn as a grid filled with numbers. It's also possible to consider the numbers of magic squares to be electric charges and to extend such analyses to higher dimensions. Loly has even calculated the so-called eigenvalues of magic squares, which are related to their "fundamental frequencies" if you were to set these squares ringing like a bell. www.sciencenews.org /articles/20060701/mathtrek.asp   (645 words)

 Magic Squares   (Site not responding. Last check: 2007-10-07) Magic Squares are a form of number pattern that has been around for thousands of years. For a pure or normal magic square, all rows, columns, and the two main diagonals must sum to the same value and the numbers used must be consecutive from 1 to n Of course this is not a pure magic square because a consecutive series of numbers from 1 to n is not used. www.geocities.com /~harveyh/magicsquare.htm   (899 words)

 Magic Square Recreations Math Science Calculates 8x8 magic squares with any given date on the first line. Publication focuses on historical and cultural attitudes towards the significance of the squares. Starting from basic operations, shows how distinct magic squares can be mathematically derived from existing ones. www.iaswww.com /ODP/Science/Math/Recreations/Magic_Square   (753 words)

 Math Games:Times Square Magic Usually, whenever magic squares come up, I will defer to Harvey Heinz's excellent Magic Squares, Magic Stars and Other Patterns website, or perhaps point to Dürer's Melencholia ("The Relativity of Albrecht Dürer" is a fascinating study). The smallest magic constant for a 3×3 multiplicative semimagic square is 120. This is a multiplication magic square: Arrange sixteen numbers in a four by four square so that the product of each row, column and corner to corner diagonal is 5,040. www.maa.org /editorial/mathgames/mathgames_11_07_05.html   (1906 words)

 Puzzle Playground - Magic Square A 7x7 square in the left part of the illustration is divided into five pieces. Now if we rearrange the pieces in the way as shown in the right part of the illustration, we will get the same 7x7 square but... with a small square hole in the center. www.puzzles.com /PuzzlePlayground/MagicSquare/MagicSquare.htm   (49 words)

 Shin's Magic Square World Magic squares have been around for over 3,000 years.. It was just a kind of puzzle for me. As time passed, I saw the solution for magic squares of odd-series and some multiples of four, and I changed my mind. But, I found out the principle of constructing squares for other sizes and checked that sums are correct by using a computer. user.chollian.net /~brainstm/MagicSquare.htm   (414 words)

 Set - How to make a magic square of Set What you see here is a magic square, much like the addition and subtraction squares you may have used as a child. These magic squares are even more talented, as they all follow the rules of the card game SET®. Not only does the magic square work but it can be theoretically proven through a mathematical model. www.setgame.com /set/magicsquare.htm   (305 words)

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