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Magic Square:     more books (100)

Learn to Crochet Easy Magic Squares by rehfeldt, 2004 Paul Klee's magic squares.: An article from: Arts & Activities by Ellen McNally, 2003-09-01 {Magic Squares} Magic Squares: Easy to Read-Easy to Make--Crochet a Pocket. Pull to Form Magic Square. --Beautifully Textured Pillows & Pot Holders. Simplified Instructions. No More Abbreviations {Coats & Clark Book No. 103} by {Magic Squares}, 1984-01-01 Magic Squares: New Methods, Embracing A General Method (1885) by James Cram, 2010-09-10 Man in a Magic Square: Poems. Magic Squares: John Horton Conway, Luca Pacioli, Magic Square, Arthur Cayley, Magic Hypercube, Siamese Method, Magic Hyperbeam, D. R. Kaprekar Games ancient and oriental,: And how to play them; being the games of the ancient Egyptians, the heira gramme of the Greeks, the ludus latrunculorum of ... draughts, backgammon, and magic squares by Edward Falkener, 1961 Magic Square Puzzles by David King, 1984-04-26 The Magic Square Tells Your Past Present Future by Walter B. Gibson, 1927 Riddles and conundrums,: Including charades, enigmas, paradoxes, anagrams, missing word puzzles, magic square and other diversions for all occasions, by Paul W Kearney, 1924 Magic Square Lexicon: Illustrated by H. D. Heinz, J. R. Hendricks, 2000 Klee: Magic Squares [Paperback]by [Klee, Paul] Muller, Joseph-Emile; 20 color by Joseph-Emile [Klee; Illustrator-20 color Paul] Muller, 1957 How Nature And Number Evolve 142857; The Magic Square Of 142857; And How 142857 Squares The Circle - Pamphlet by Willis F. Whitehead, 2006-09-15 Magic Squares: 92 Puzzles for You to Solve! by Raymond Tidd, 2009-09-17

lists with details

61. Ivars Peterson's MathLand: More Than Magic Squares
    Introduction with reference to Victor Hill and Bach.  
    http://www.maa.org/mathland/mathland_10_14.html
    
    Extractions: Ivars Peterson's MathLand October 14, 1996 "In my younger days, having once some leisure (which I still think I might have employed more usefully), I had amused myself in making . . . magic squares." Benjamin Franklin, who made this comment in a letter written more than 200 years ago, was certainly not the first to experience the fascination of magic squares. People have been toying with these number patterns for more than 2,000 years. Typically, a magic square consists of a set of integers arranged in the form of a square so that the sum of the numbers in each row, each column, and each diagonal add up to the same total. If the integers are consecutive numbers from 1 to n ^2, the square is said to be of n th order. Here's an example of a magic square of the fourth order, made up of the first 16 integers. The sum of the numbers in each row, column, and diagonal is 34. There are 880 possible magic squares of the fourth order, not counting reflections or rotations of each pattern. One of the most remarkable of these squares is one that dates back to India in the eleventh or twelfth century. Notice that not only the rows, columns, and diagonals add up to 34 but also the corner 2 x 2 subsquares. And there's more! The four corner numbers add up to 34, as do the four numbers in the center. Other subsquares (such as 3 + 10 + 6 + 15) give the same result. It's also possible to find "split" subsquares and "split" diagonals that work: 7 + 2 + 14 + 11, and so on. In fact, there is an astonishing number of different ways to get the sum 34 out of this particular magic square.

62. Multimagic Squares
    Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)  
    http://www.multimagie.com/

63. Backtracking: 5 X 5 Magic Squares
    Interactive 5x5 magic square generator using backtracking algorithm. The user can move the numbers manually, watch the computer slowly creating a magic  
    http://www.faust.fr.bw.schule.de/mhb/backtrack/mag5en.htm
    
    Extractions: A mouseclick on any number of the green-bordered square ("number-pool") moves this number into the first empty field of the red-bordered square ("magic area"); a click on any number of the magic area brings the number back to its original place in the pool. Aim A magic square of order 5 is to be constructed, depending on choice a panmagic and/or a symmetric or a bordered one. When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by clicking the option "mouse". When a solution is found, the algorithm will stop, and in that case, a search for a next solution may be continued with the corresponding button. The blue-bordered square always contains the last found solution.

64. Magic Squares Of Order 4
    Interactive 4x4 magic square generator using backtracking algorithm. The user can move the numbers manually, watch the computer slowly creating a magic  
    http://www.faust.fr.bw.schule.de/mhb/backtrack/mag4en.htm
    
    Extractions: A mouseclick on any number of the green-bordered square ("number-pool") moves this number into the first empty field of the red-bordered square ("magic area"); a click on any number of the magic area brings the number back to its original place in the pool. Aim A magic square of size 4 x 4 is to be constructed, depending on choice a general, a panmagic or a symmetric one. When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by clicking the option "mouse". If the Stop-option is activated, the algorithm will stop, whenever a solution is found, and in that case, a search for a next solution may be continued with the corresponding button. The blue bordered square always displays the last found solution. The delay (in milliseconds) regulates the frequency of image output, if "show" is activated. H.B. Meyer

65. 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.ouh.nl/open/eyn/applets/magicsq.htm

66. Interactive Magic Square 3x3
    Hope you like this 3 x 3 magic square!! Find out more about magic squares. View Benjamin Franklin s 8x8 magic square in animation  
    http://www-personal.une.edu.au/~lgrunwa2/une/KLAs/maths/magic3x3.html

67. Magic Square -- From MathWorld
    magic square Wikipedia, the free encyclopediaA normal magic square contains the integers from 1 to n². magic squares exist for all orders n = 1 except n = 2, although the case n = 1 is trivial—it  
    http://www.astro.virginia.edu/~eww6n/math/MagicSquare.html
    
    Extractions: MATHWORLD - IN PRINT Order book from Amazon Recreational Mathematics Magic Figures Magic Squares ... Matrix Types Magic Square A magic square is a square array of numbers consisting of the distinct positive integers arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number (Kraitchik 1952, p. 142; Andrews 1960, p. 1; Gardner 1961, p. 130; Madachy 1979, p. 84; Benson and Jacobi 1981, p. 3; Ball and Coxeter 1987, p. 193), known as the magic constant If every number in a magic square is subtracted from , another magic square is obtained called the complementary magic square. A square consisting of consecutive numbers starting with 1 is sometimes known as a "normal" magic square. The unique normal square of order three was known to the ancient Chinese, who called it the Lo Shu . A version of the order-4 magic square with the numbers 15 and 14 in adjacent middle columns in the bottom row is called . Magic squares of order 3 through 8 are shown above. The magic constant for an th order general magic square starting with an integer and with entries in an increasing arithmetic series with difference between terms is (Hunter and Madachy 1975).

68. Merlin's Magic Squares
    a magic squares game with a Linear algebra Background.  
    http://www.cut-the-knot.org/ctk/Merlin.shtml
    
    Extractions: by Alex Bogomolny April 1998 In Merlin's Magic Square , an article that appeared in The American Mathematical Monthly in 1987, Don Pelletier explored the mathematical apparatus behind a toy game known as MERLIN . The game is not quite trivial and the mathematics is simple enough to provide an entertaining exercise in a Linear Algebra class. The original game is played on a 3x3 array of buttons that toggle between two states. The goal of the game is to achieve a target configuration of button states by pressing the buttons. The difficulty lies in that pressing a button alters its state but also toggles states of some neighboring buttons. The applet below generalizes the game in three ways: Buttons are multistate, The target configuration is modifiable, The manner in which pressing a button affects its neighbors is selectable. The applet consists of two 3x3 arrays. On the left, the small one shows the target configuration. To modify the target configuration, click on the squares you want modified. On the right, a bigger one holds the puzzle itself and, if the

69. Magic Squares Game
    A game with a Linear Algebra background.  
    http://www.cut-the-knot.org/game_st.shtml

70. Magic Squares Applet
    Please Note This applet, which is an update of the original magic squares Applet, has been having problems running on the following system configurations  
    http://www.mste.uiuc.edu/java/michael/magicsquares/

71. SquareMaker To Design A Magic Square Or A Sudoku
    pivari.com SquareMaker a simple tool to create magic square png. Introduce your magic square (every number separated by ,). 5,31,35,60,57,34,8,30,  
    http://www.pivari.com/squaremaker.html

72. Magic Squares
    A magic square is a rectangular array of numbers, usually from 1 to n2, One of the most famous illustrations of a magic square is in the famous  
    http://www.pballew.net/magsquar.html
    
    Extractions: Magic Squares    A "magic square" is a rectangular array of numbers, usually from 1 to n so that each column, row, and both diagonals have the same sum.  Other types of magic squares, with other shapes or special properties are common in recreational math.  You can find a very great number of examples of different squares and special features at the web site of Harvey Heinz with additional information on magic stars.   The history of magic squares dates back to at least 1000 BC in China.  A Chinese book called Lo Shu (book of the River Lo) relates the story of how a magic square on the back of a turtle saved the city.  By the 2nd Century BC there were 4x4 magic squres appearing, often in connection with religious practice.  The Islamic/Arab mathematicians probably were introduced to the magic square from India, but they quickly developed squares of higher order.  One of the most famous illustrations of a magic square is in the famous Albrecht Durer woodcut, Melancholia.  The illustration and a blow up of the square can be seen at these links to the St Andrews University site.  Durer was a major contributor to the mathematics of art and is often credited with being the founder of descriptive geometry, yet he is probably known to most students, if at all, for this single woodcut. There are 880 different solutions to the 4x4 magic square, including the one in the Durer painting.

73. The JavaScript Source: Games: Magic Squares
    Here is a fun JavaScript game. Try to put the squares back in order. The 0 repesents the empty spot, and click a square next to the 0 to make them trade  
    http://javascript.internet.com/games/magic-squares.html
    
    Extractions: Submit Your Script! White Paper: Information Management Trends In 2005 What's your current data focus? While some companies are still focused on storage and access, others are leveraging their information to be more agile, gain new insights into business performance and make better decisions. Get this white paper and learn how your peers are implementing their data management solutions.

74. Magic Square
    http://www.smilemathematics.co.uk/flash/magicsq.html

75. Magic Squares
    This method gives only 1 magic square for any N. There are many others. Methods of creating even magic squares are known, but are not this elegant.  
    http://uzweb.uz.ac.zw/science/maths/zimaths/magic.htm
    
    Extractions: Have you ever given someone a problem which they can't solve after hours, when you can produce an answer in a matter of minutes? If not, here's your chance! A magic square is a N x N array of cells, each cell containing one of the first N positive integers, such that the sum of the numbers along any row, column and the two diagonals is a constant. De la Loubere was the French Ambassador to Thailand in 1687-1688 when he learnt the following method for odd values of N. Write 1 in the middle cell of the top row. Now keep writing 2,3,4,... in the up-right direction. If you reach the end of the square, `come out' on its opposite side. If you have to write on a used square, go down one cell. For example, here is a 7 by 7 magic square. This method gives only 1 magic square for any N. There are many others. Methods of creating even magic squares are known, but are not this elegant. Now, go and ask your best friend to create a 99 by 99 magic square... Back to Zimaths Issue 1.4

76. Magic Squares - Mathematics And The Liberal Arts
    (3) magic squares may first occur in the lo shu diagram, which is often linked The author discusses how the idea of magic squares may have entered the  
    http://math.truman.edu/~thammond/history/MagicSquares.html
    
    Extractions: To expand search, see Arithmetic and Mathematics and Mysticism . For material on related topics, see The Square . Laterally related topics: Number Systems Numerology Bookkeeping Modular Arithmetic ... Astrology , and Pseudoscience The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Biggs, N. L. The roots of combinatorics.

77. TeacherSource . Math . Magic Squares And Stars | PBS
    Themebased units for K-12 math teachers, including classroom activities and career connections showing how math is used in everyday life.  
    http://www.pbs.org/teachersource/mathline/concepts/historyandmathematics/activit
    
    Extractions: Answers (PDF File) Activity 2 This elementary activity can be used at higher levels by having students determine all possible combinations of 4 digits between 1 and 12 inclusive whose sum is 26 (there are 32) and then creating as many magic stars as they can using their list. Magic Squares and Stars For centuries, mathematicians and individuals interested in recreational mathematics have been interested in magic squares. Practically all historians agree that the magic square had is origin in China centuries before the birth of Christ. The exact origin has been lost, but Oriental tradition holds that the Emperor Yu (c.2200 B.C.) was standing on the bank of the Yellow river when a tortoise appeared with a mystic symbol on its back. This figure came to be know as the

78. Solution For /arithmetic/magic.squares
    Solution to the /arithmetic/magic.squares problem. These are called magic squares. A magic square of order n (integers from 1 to n*n) has only one possible  
    http://rec-puzzles.org/sol.pl/arithmetic/magic.squares
    
    Extractions: These are called magic squares. A magic square of order n (integers from 1 to n*n) has only one possible sum: (n*n+1)*n/2. Odd and even order squares must be constructed by different approaches. For odd orders, the most common algorithm is a recursive scheme devised by de la Loubere about 300 years ago. For even orders, one procedure is the Devedec algorithm, which treats even orders not divisible by 4 slightly differently from those which are divisible by 4 (doubly even). For squares with odd-length sides, the following algorithm builds a magic square: Put 1 in the middle box in the upper row. From then on, if it's possible to put the next number one box diagonally up and to the right (wrapping around if the edge of the grid is reached), do so, otherwise, put it directly below the last one. ...or even See archive entry knight.tour for magic squares that are knight's tours. To get a 4x4 square, write the numbers in order across each row, filling the square... then use the following pattern as a mask: . X X . X . . X X . . X . X X .

79. LoneWolf's Lair: Magic Squares
    A magic square is an NxN grid that contains all of the numbers from 1 to N2 This application will generate the magic square for the dimension that you  
    http://www.sightspecific.com/~mosh/Tricks/MagicSquare/
    
    Extractions: Magic Squares A magic square is an NxN grid that contains all of the numbers from 1 to N (N-squared) in such a way that the sum of all of the numbers from any row, column, or diagonal equals the same number. For example, a 3x3 grid would contain all of the numbers from 1 to 9 (3-squared) such that, were you to add the numbers from any row, column, or diagonal, the sum would equal 15. Go ahead and enter an odd, positive number in the form field below, click the build button, and see for yourself. This application will generate the magic square for the dimension that you enter. That is, if you enter 3, it will display the 3x3 magic square. Dimension: This page was last updated Monday, February 8, 1999.

80. Magic Squares
    magic squares may be perhaps the only area of recreational mathematics to which The classic form of a magic square is a square containing consecutive  
    http://members.shaw.ca/quadibloc/math/squint.htm
    
    Extractions: Home Other Mathematics Magic Squares may be perhaps the only area of recreational mathematics to which many of us have been exposed. The classic form of a magic square is a square containing consecutive numbers starting with 1, in which the rows and columns and the diagonals all total to the same number. I'll have to admit that I was never very much interested by magic squares, as opposed to other mathematical amusements, but a Mathematical Games column in Scientific American by Martin Gardner disclosed some new discoveries in magic squares that are of interest. The only magic square of order 3, except for trivial translations such as reflection and rotation, is: Some magic squares are very simple to construct. Magic squares of any odd order can be constructed following a pattern very similar to that of the 3 by 3 magic square: One can also construct a magic square by making a square array of copies of a magic square, and then adding a displacement to the elements of each copy based on a plan given by another magic square: thus, making nine copies of

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