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Magic Square:     more books (100)

The Mystic Fortune Teller with the Magic Square by Walter B. Gibson, 1927 Mexico's Magic Square by Erle Stanley Gardner, 1968 Fundamental Computations for Magic Squares by Philip Wagala Gwanyama, 2010 Mexico's Magic Square, Adventure Just South of the Border in Baja California Mathemagic: magic squares and other designs. by Royal Vale. Heath, 1988 Games ancient and oriental and how to play them, being the games of the ancient Egyptians, the Hiera Gramme of the Greeks, the Ludus Latrunculorum of the ... draughts, backgammon and magic squares by Edward Falkener, 2010-08-30 Easy to Read, Easy to Make Magic Squares Book No. 103 by Coats & Clark, 1984 THE WONDERS OF MAGIC SQUARES by Jim Moran, 1982-01-01 Ben Franklin and the Magic Squares   [BEN FRANKLIN & THE MAGIC S] [Paperback] Magic Square Numbers (A Reflection book) by J. R. King, 1963-01-01 Easy Methods for the Construction of Magic Squares by J. C Burnett, 1936 Simple Magic Square The Mystic Fortune Teller: With The Magic Square by Walter Gibson, 2010-09-10 Magic square: An entry from Thomson Gale's <i>Gale Encyclopedia of Science, 3rd ed.</i> by Jeanette Vass, 2004

lists with details

81. A Very, Very Magic Square
    A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.  
    http://www.math.lsa.umich.edu/~hderksen/magic.html

82. Nrich.maths.org :: Mathematics Enrichment :: Magic Squares
    For the simple 3x3, that is order 3 magic square, trial and improvement quickly Sequentially place the numbers 1 to n 2 of the n x n magic square in the  
    http://nrich.maths.org/1337
    
    Extractions: If so we'd love to involve you in our research. Are you aged between 10 and 17? Read about Dr Yi Feng's research which involves talking to students over the next two years about their mathematical experiences in and out of school, and respond to the call for participants. Do you use the ASKNRICH site, or have you previously? Libby Jared's research involves looking at what goes on on the ASKNRICH site and why. To help with this research please respond to the ASKNRICH survey Read more about the research we are doing here Magic squares have intrigued people for thousands of years and in ancient times they were thought to be connected with the supernatural and hence, magical. Today, we might still think of them as being magical, for the sum of each row, column and diagonal is a constant, the magic constant. The squares intrigued me when I found that their construction was far from easy. For the simple 3x3, that is order 3 magic square, trial and improvement quickly does the job; but for higher than order 4 magic squares a method is necessary. The problem of construction is twofold. An algorithm which works for odd order squares will not work for even order squares without the further addition of another algorithm. At least, I know of no method which will work for both odd and even orders, other than trial and improvement computer programs. For the purposes of this article, I will be considering only magic squares that are constructed using consecutive integers from 1 to

83. Magic Square — Infoplease.com
    Encyclopedia magic square. magic square, a square divided into parts with letters or numbers inscribed therein that, whether combined vertically, horizontally, or diagonally, form the  
    http://www.infoplease.com/ce6/society/A0831139.html

84. Finding Magic Squares Using CCM
    The Chemical Casting Model (CCM) generation method is demonstrated with a Java Applet. Source code and description of algorithm included. (English/Japanese) JRE required for Applet only.  
    http://www.kanadas.com/ccm/magic-square/index.html
    
    Extractions: Japanese version [English version] [Temporary Mirror Page (Fast!)] [Original Page (Newer?!)] Magic squares of degree N is a collection of N by N columns, which contain integers from 1 to N . The sum of N integers of all the columns, all the rows, or a diagonal must be the same. A method of finding a magic square using CCM is explained here. The applet below searches for a magic square. If you used this applet in its initial state, you can track the process by your eye in some extent. (If this applet is too large, you can use this small applet If you change the option value, which is ``medium speed (20 rps)'' in its initial state, to ``full speed,'' the computation will be done as quick as possible. (20 rps means that the rule is applied 20 times per second (rps = reductions per second). However, the real rps is less than 20.) You can start the computation again using the ``restart'' button. You probably find a different solution each time because random numbers are used, and the computation time is also different each time. If you change the option, which is set to ``swapping rule'' initially, then you can change the production rule. The rules are explained in

85. Magic Squares ROCK!
    Explores the physical aspects of magic squares. A mass model demonstrates unique properties associated with the moment of inertia for the square. The topographical model looks at water retention patterns in the square.  
    http://www.knechtmagicsquare.paulscomputing.com/

86. Magic Square Definition By Babylon's Free Dictionary
    Definition of Magic square square divided into smaller numbered squares so that that every row and column adds up to the same total  
    http://dictionary.babylon.com/magic square/

87. Magic Square Java Applet
    A documented Java applet that generates Magic Squares using a given starting number, increment, and starting location. Row, column and diagonal sums are displayed on request. Odd orders up to 7 are accepted. JRE required  
    http://www.open.ou.nl//eyn/applets/magicsq.htm

88. The Anti-Magic Square Project
    Starting from the definition of an Anti-Magic Square (AMS), the article presents the structure and construction methods of the AMS. Programs written in the c-language are available for download.  
    http://ion.uwinnipeg.ca/~vlinek/jcormie/
    
    Extractions: The Anti-Magic Square Project This web site documents my 1999 summer research on a combinatorial design called the Anti-Magic square. Anti-Magic Squares are a variation on the heavily studied and well-understood magic square. In contrast, very little seems to be known about AMSs. These pages describe what was previously known about the structure and history of the AMS and also detail new discoverys regarding their enumeration and construction. Thanks for your patience and understanding, as this page is still under construction! An Anti-Magic Square (AMS) is an arrangement of the numbers 1 to n in a square matrix such that the row, column, and diagonal sums form a sequence of consecutive integers. The arrangement to the left is Anti-Magic because sorting the sums (numbers in black on the border) yields the sequence: 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269 This is an example of an AMS(8), or Anti-Magic Square of order 8, which comes from Madachy's Mathematical Recreations Given this definition, this research project aims to answer some of the following questions:

89. Muse: Magic Squares, Science News For Kids: MatheMUSEments
    of Durer s square and an alphamagic square.  
    http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse1103.asp
    
    Extractions: Search MatheMUSEments Magic Squares By Ivars Peterson Muse , November/December 2003, p. 32-33. Do you have a lucky number? In ancient China, people believed that a special arrangement of nine numbers in a square was especially lucky. They engraved this pattern on stones or medallions that were worn as charms to ward off evil or bring good fortune. Here's the pattern. Can you tell what's special about it? Notice it contains all the numbers from 1 to 9. Better yet, the numbers in each row, column, and diagonal add up to 15. Arrangements of numbers that add up to the same total in every row, column, and diagonal are known as magic squares. Melancholia , an engraving by the German artist Albrecht Dürer, includes a famous magic square. The rows, columns, and main diagonals all sum to 34. The magic square is hanging on the wall to the upper right. Not only do the rows, columns, and diagonals total 34, so do the numbers in the corner squares and the numbers in the central four squares. Can you find other combinations within the square that add to 34? There are several. For example, If you divide the four-by-four square into four two-by-two squares, each of those squares will add up to 34. What's more, the numbers in the middle bottom squares read 1514, the year Dürer made the engraving.

90. Mutsumi Suzuki: Magic Stars
    Introduction to Magic Stars. Construction, analysis and transformations.  
    http://mathforum.org/alejandre/magic.star/
    
    Extractions: Suzanne Alejandre and Mutsumi Suzuki's Suzanne's Math Lessons Magic Squares Tessellation Tutorials Mutsumi Suzuki is Professor of Engineering in the Laboratory for Process Systems Engineering, Tohoku University, Sendai, Japan. His research interests include reduced gravity and chemical engineering, and process system engineering. Magic Squares are one of his hobbies, of which the magic stars outlined on these pages are an extension.

91. Making Magic Squares -- Math Fun Facts
    A magic square is an NxN matrix in which every row, column, and diagonal add up to the same number. Ever wonder how to construct a magic square?  
    http://www.math.hmc.edu/funfacts/ffiles/10001.4-8.shtml
    
    Extractions: Figure 2 A magic square is an NxN matrix in which every row, column, and diagonal add up to the same number. Ever wonder how to construct a magic square? A silly way to make one is to put the same number in every entry of the matrix. So, let's make the problem more interesting- let's demand that we use the consecutive numbers I will show you a method that works when N is odd. As an example, consider a 3x3 magic square, as in Figure 1. Start with the middle entry of the top row. Place a 1 there. Now we'll move consecutively through the other squares and place the numbers 2, 3, 4, etc. It's easy: after placing a number, just remember to always move: 1. diagonally up and to the right when you can

92. Magic Cubes And Tesseracts
    Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)  
    http://homepage2.nifty.com/googol/magcube/en/

93. The Magic Square
    E 6 Up Exceptional Lie Algebras Previous F 4 4.3 The Magic Square Around 1956, Boris Rosenfeld had the remarkable idea that just as is the isometry group of the projective  
    http://math.ucr.edu/home/baez/octonions/node16.html
    
    Extractions: 4.3 The Magic Square Around 1956, Boris Rosenfeld [ ] had the remarkable idea that just as is the isometry group of the projective plane over the octonions, the exceptional Lie groups and are the isometry groups of projective planes over the following three algebras, respectively: There is definitely something right about this idea, because one would expect these projective planes to have dimensions 32, 64, and 128, and there indeed do exist compact Riemannian manifolds with these dimensions having and as their isometry groups. The problem is that the bioctonions, quateroctonions and and octooctonions are not division algebras, so it is a nontrivial matter to define projective planes over them! The situation is not so bad for the bioctonions: is a simple Jordan algebra, though not a formally real one, and one can use this to define in a manner modeled after one of the constructions of . Rosenfeld claimed that a similar construction worked for the quateroctonions and octooctonions, but this appears to be false. Among other problems, and do not become Jordan algebras under the product . Scattered throughout the literature [ ] one can find frustrated comments about the lack of a really nice construction of and . One problem is that these spaces do not satisfy the usual axioms for a projective plane. Tits addressed this problem in his theory of `buildings', which allows one to construct a geometry having any desired algebraic group as symmetries [

94. The Math Behind The Siamese Method Of Generating Magic Squares
    The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.  
    http://www.xs4all.nl/~thospel/siamese.html
    
    Extractions: A magic square consists of the distinct positive integers 1, 2, ... n , such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same magic constant. If the rows and columns sum to the magic constant (so ignoring the main diagonals) it is called a semimagic square. Several ways exist to automatically generate magic squares, among which the most famous one is the Siamese method to generate odd-sized magic squares. It is also called the de la Loubere's method. The method is purported to have been first reported in the West when de la Loubere returned to France after serving as ambassador to Siam. This example is taken from the excellent description on Math Forum . I reproduce it almost literally here in case that link ever goes away. Start with an empty n x n square, where n is odd . We'll begin with n = 5 and denote its blank entries with dots.

95. Magic Square
    Arrange the numbers 1 through 9 in a 3 by 3 array a Magic Square such that the sum of any row, column, or the two diagonals is the same. Is your solution unique?  
    http://jwilson.coe.uga.edu/emt725/BotCan/Magic.html

96. Magic Cubes
    The site presents a program for finding all possible order 3 cubes, executable and source included.  
    http://www.delphiforfun.org/Programs/Source_Listings/MagicCubeSource.html

97. Magic Square - Definition Of Magic Square By The Free Online Dictionary, Thesaur
    The kids not just quickly explain the meaning after the song but also present a Magic Square equation in the blink of an eye.  
    http://www.thefreedictionary.com/magic square

98. The Zen Of Magic Squares, Circles, And Stars:
    Features reviews, information and index of Clifford A. Pickover s book. Publication focuses on historical and cultural attitudes towards the significance of the squares.  
    http://sprott.physics.wisc.edu/pickover/zenad.html
    
    Extractions: Ian Stewart, University of Warwick Order from Amazon.com. "At first glance magic squares may seem frivolous (Ben Franklin's opinion, even as he spent countless hours studying them!), but I think that is wrong. The great nineteenth-century German mathematician Leopold Kronecker said 'God Himself made the whole numberseverything else is the work of men,' and Cliff Pickover's stimulating book hints strongly at the possibility that God may have done more with the integers than just create them. I don't believe in magic in the physical world, but magic squares come as close as we will probably ever see to being mathematical magic."

99. Grogono Magic Squares Home Page
    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  
    http://www.grogono.com/magic/index.php
    
    Extractions: Revisions A Magic square is intriguing; its complexity challenges the mind, certainly more than games like online bingo . For order 4 and above the number of different magic squares is astonishing - and the number remains large even if we limit consideration to Pan-Magic squares. This website reflects my own fascination with these large numbers and presents techniques aimed at explaining and reducing the huge numbers by showing how this abundance can be reduced to a small number of underlying patterns or Magic Carpets Do it yourself! This is now working again. Changes in the language had stopped it working for a while. Make your own magic square of any size up to 97x97. The development of this website was associated with several intriguing discoveries. Please look at the pages for the Order 4 Order 5 Order 6 magic squares.

100. Redirect
     Presents the Magic Carpet approach by Grog . Downloads available for analyzers and creators in Excel format.  
     http://www.grogono.com/Magic/

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