1. The Magic Square Record Includes short description of a magic square, rules for trying to break a magic square record and all the records between 1975 and now. http://www.recordholders.org/en/records/magic.html

The Largest Magic Square A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum. Example: (sum is 15 for each row, column and diagonal) You can read more about magic squares at forum.swarthmore.edu/alejandre/magic.square.html 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 The Rules The magic square must be written/printed on paper. It is not sufficient just to calculate it by a computer. It is allowed to compose the magic square from many sheets of paper, but they MUST lay together to form one scheme of numbers. This scheme must be a square, not just any rectangle. To verify the sums in each row/column and diagonal a test run of the used computer program should be made under supervision of a computer/ mathematics specialist who can prove that the program is correct. The World Recordss Largest Magic Square Written by Hand 1111 X 1111 Norbert Behnke (Krefeld, Germany) 1990

2. Simple Magic Square Checker And Gif Maker Simple magic square checker and gif maker. http://www.geocities.com/CapeCanaveral/Lab/3469/squaremaker.html

Simple Magic Square checker and gif maker by Fabrizio Pivari version 4.3 1997/06/19 Magic square elements (each separated by Default is blank): (Note: you can use letter and negative numbers.) Functions Skip blanks Magic Square gif Magic Square table Magic Square check (Semimagic Square, Magic Square, Panmagic Square with Magic Constant = n(n +1)/2 or different) Miscellaneous Image Method Interlaced GIF Colours Transparent Background Background Colour in RGB mode Foreground Colour in RGB mode Utilty from Palette to RGB Press to submit your query. The option Magic Square check for normal Magic Square (1,2,...N) now generate the gif of Magic Line (a line that connects every number form 1 to N) After saving your Magic Square you can use the gif to create a magic square Texture Map in VRML Examples made with this tool Source Code You can also find the source code at CPAN authors/Fabrizio_Pivari/ From version 4.0 in the source code you can find a PERL program with the same features of this CGI-BIN script Links around the world to this page Yahoo Science:Mathematics:Games:Combinatorics The Perl Oasis archive Magic Square by Eric Weisstein in Eric's Treasure Trove of Mathematics Magic Squares by Mutsumi Suzuki Magic Squares by Suzanne Alejandre Math Forum Internet Resource Collection by Web Master

3. Math Forum: Suzanne Alejandre: Magic Squares Resources for including magic squares in the curriculum, with activities for students and explanations Category Science Math Recreations magic square...... What is a magic square? Allan Adler defines and discusses some specialproperties of magic squares. Mike Morton's magic square Java Applet. http://mathforum.org/alejandre/magic.square.html

A Math Forum Web Unit Suzanne Alejandre's Magic Squares Suzanne's Math Lessons Suzanne's Tessellation Lessons Magic squares received their name because there are so many relationships between the sums of the numbers filling the squares. Students often believe that "mathematics" was "written" by one person. In these pages you will find that the magic square mathematical game has existed throughout history and in many different parts of the world. Math is all around us and your mind will see it when you're ready! What is a Magic Square? Allan Adler defines and discusses some special properties of magic squares. Magic Squares - History, Mathematics, Geography Lo Shu Magic Square The Back of the Divine Tortoise Classroom Activity China - the country of Lo Shu ... Rome, Italy - the country of the Sator Where's the Math? - with Allan Adler Classroom activities: multiplying magic squares Constructing magic squares Defining the magic square; special properties ... Review: Squaring a magic square Mike Morton's Magic Square Java Applet Dubi Kaufmann's Magic Square Puzzle H. B. Meyer's

4. LogoMation An easy to learn computer programming environment. Write programs that tell the computer to draw things. 21day trial. http://www.magicsquare.com/LM2/

LogoMation : A Computer Language for Education If you arrived here looking for the LogoMation Sports Screen Saver , click HERE LogoMation is an easy to learn computer programming environment. It is available on Window (95, 98, NT 4.0, Win2000), and on Macintosh. The included LogoMation book provides step-by-step, clear and easy to follow instructions on using the development environment. LogoMation is for Middle and high-School students, learning computer programming. College-level introductory computer science courses. People who never programmed a computer, and always wanted to try. Seasoned programmers who want to have fun with animation. Please click on the buttons on the left to learn more about LogoMation. LogoMation support: Support@MagicSquare.com Questions and information: info@MagicSquare.com

5. Dubster.com - Magic Square Puzzle In this puzzle the goal is to have the total of each row and column to beequal to 30. Click on a piece to pick it up and click again to drop it. http://www.dubster.com/math/

In this puzzle the goal is to have the total of each row and column to be equal to 30. Click on a piece to pick it up and click again to drop it. This puzzle has been conceived and executed by Dubi Kaufmann contact math2@dubster.com for information or try the FAQ

6. A Very, Very Magic Square Includes a 25x25 magic square, properties of it and Maple and PostScript files for finding more propertie Category Science Math Recreations magic square......A very, very magic square. The following square. There is also a postscriptfile magicsqr.ps and a dvifile magicsqr.dvi of the magic square. 1, http://www.math.lsa.umich.edu/~hderksen/magic.html

A very, very magic square The following 25x25 matrix is a magic square.It has the following properties: Then entries of the square are the numbers 1,2,...,625=25x25. All its column sums, row sums and both diagonal sums are all equal to 7825=25x(1+625)/2. 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. Maybe you will find out even more properties.... Here is a maple program to generate this 25x25 square. There is also a postscript file magicsqr.ps and a dvi-file magicsqr.dvi of the magic square. Back to my homepage

7. Math Forum: Allan Adler - What Is A Magic Square? What is a magic square? In the case of this 4x4 magic square in addition tohaving the sum 34 (= 4(4^2+1)/2) in each row, column and main diagonal, http://mathforum.org/alejandre/magic.square/adler/adler.whatsquare.html

A Math Forum Web Unit Allan Adler's What is a Magic Square? Suzanne's Magic Squares Multiplying Magic Squares: Contents Exploring the Math Definition, Special Properties A magic square is an arrangement of the numbers from to n^2 (n-squared) in an n x n 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. It is not hard to show that this sum must be n(n^2+1)/2 The simplest magic square is the magic square whose only entry is the number The next simplest is the magic square and those derived from it by symmetries of the square. This square is definitely magic and satisfies the definition given above. The (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. They are so interesting that they are often pointed out when this square is presented. That is good, but can sometimes lead to misunderstandings as to which is the meat and which is the gravy. The meat is the definition I gave above. The gravy (or some of it), suggested by Jerome S. Meyer in his book, Fun with Mathematics

8. Magic Square -- From MathWorld magic square, A version of the order 4 magic square with the numbers 15 and 14 inadjacent middle columns in the bottom row is called Dürer's magic square. http://mathworld.wolfram.com/MagicSquare.html

Foundations of Mathematics Mathematical Problems Unsolved Problems Recreational Mathematics ... Magic Squares Magic Square A (normal) magic square consists of the distinct positive integers such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same magic constant If every number in a magic square is subtracted from , another magic square is obtained called the complementary 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 n th order magic square starting with an integer A and with entries in an increasing arithmetic series with difference D between terms is (Hunter and Madachy 1975). It is an unsolved problem to determine the number of magic squares of an arbitrary order, but the number of distinct magic squares (excluding those obtained by rotation and reflection) of order n = 1, 2, ... are 1, 0, 1, 880, 275305224, ... (Sloane's

9. Recmath Home Page Includes pages on magic squares and polyomino patterns and contains related java applets. http://web.idirect.com/~recmath/

Puzzle Page Patterns and Magic Squares (1) Patterns and Magic Squares (2) ... Patterns mail Last Updated on May 9th 2001 Web Counted visits since May 9th 2001:

10. Dürer's Magic Square -- From MathWorld Dürer's magic square, Dürer's magic thought. Dürer's magic squareis located in the upper righthand corner of the engraving. The http://mathworld.wolfram.com/DuerersMagicSquare.html

Recreational Mathematics Magic Squares Recreational Mathematics Mathematical Art ... magic square with magic constant 34 used in an engraving entitled Melancholia I et al. gnomon magic square Gnomon Magic Square Magic Square References Boyer, C. D. and Merzbach, U. C. A History of Mathematics. New York: Wiley, pp. 296-297, 1991. Burton, D. M. Cover illustration of Elementary Number Theory, 4th ed. Boston, MA: Allyn and Bacon, 1989. VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989. Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, 1975. Ollier, T. " Melancholia I, by Albrecht Durer: Detail and Annotation of Symbolism." http://www.pensword.com/durer.html Rivera, C. "Melancholia." http://www.primepuzzles.net/melancholia.htm Author: Eric W. Weisstein Wolfram Research, Inc.

11. Education 4 Kids Sponsored By WellCenter (a Free Educational Resource) Note This was called magic square , but the name has been changed since it wasnot really a magic square where all rows, columns and diagonals added up to http://www.edu4kids.com/msq/

Sponsored by: WellCenter Healthy minds, healthy bodies. SPECIAL OFFERS from Hooked on Phonics and Scholastic FlashCards Math Square Math Tables ... Money Experience Math Square Welcome to the Math Square. The directions are simple. In each square put numbers until the total for the row (if you add up all the numbers) is equal to the value next to the row. Make sure you get the right values in each column and in the diagonal direction too! To see what it looks like, look below Note: This was called "Magic Square", but the name has been changed since it was not really a "magic square" where all rows, columns and diagonals added up to the same number. We offer three versions of this game. The first just uses numbers 1-9, the second lets you enter the starting number and then uses the next 8 numbers, and the third uses a set of random digits between 1-99. In all cases the center digit is filled in for you. No digit is used twice. We have added a nice feature that shows the numbers that are used in the Math Square. If you want to play the hard version really hard, play it without seeing the numbers. If you want to play it easier, turn on the numbers (they will be displayed above the game). Have fun! Starting Number: Show The Numbers Don't Show The Numbers If you like the site, please take the time to share it with your friends. We have even created a

12. Allmath.com - Magic Squares Game In the easy level, you are given the numbers beginning from one and must createa magic square. How large would you like the magic square to be on each side? http://www.allmath.com/magicsquare.asp

Option Explicit allmath.com Allmath Homepage Math Tools Flash Cards!!! Metric Converter Games The Magic Square Reference Pages Biographies of Math Math Glossary Multiplication Table Metric Conv. Factors ... Ask The Experts Visit our Dictionary! ALLwords.com About allmath.com Welcome! Privacy Statement Who are We? Advertise 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. If you know how to play, you can use the square below. Otherwise, read the instructions and fill in the form at the bottom to begin a new game. Numbers to use: Numbers you have used: In this game, you must fill in the magic squares. In the easy level, you are given the numbers beginning from one and must create a magic square. The medium difficulty level is similar, but instead of getting each row, column, and diagonal to add to the same value, each one has a different value which is given to you. In the hard level, you are given random numbers, some positive and some negative, and you must place them in the square to get the sums given to you. To start playing, you first select whether you want a 3 by 3 square, 4 by 4 square, or 5 by 5 square. As the square gets bigger, the puzzle becomes more difficult. Next, you select the difficulty level you wish to play.

13. Magic Square Models CONTENTS A Crossstitched magic square. of order-5 (but lots of combinations). Order-4magic square. constructed with wooden blocks and dowels. http://www.geocities.com/CapeCanaveral/Launchpad/4057/ms_models.htm

M agic Square Models On this page I show photographs of handicraft projects made using magic squares, magic stars and related subjects as the theme. It is a rewarding experience to hold, for example, an actual 3 dimensional model of a magic star or cube, instead of simply viewing a 2 dimensional version of it on paper. Unfortunately, a photograph simply reverses the process, and we are once again viewing a 2 dimensional version of the object. CONTENTS A Cross-stitched Magic Square of order-5 (but lots of combinations). A Cross-stitched Magic Star of order-6. Points also are magic. A Pandiagonal Torus Any pandiagonal magic square may be considered as being on the surface of a torus in stead of a plane. Order-4 Magic Square constructed with wooden blocks and dowels A Wooden Magic Cube of order-3. Magic lines shown with dowels. A Wooden 3-D Magic Star An 8-point star with 12 lines of 3 numbers sum to 27. A Wooden 3-D Magic Star- 2 As above, but 3 missing numbers inserted to now give 22 lines summing correctly. A Number Pattern 12 = 3 x 4, 56 = 7 x 8, 9 is not equal to 0.

14. Magic Square, Inc. marketing . mktg@MagicSquare.com. Founded in 1996, magic square Inc. developspowerful Internet technologies, and educational software. Visit the L3 site. http://www.magicsquare.com/

general information.... info@MagicSquare.com tech support.... support@MagicSquare.com marketing.... mktg@MagicSquare.com Founded in 1996, Magic Square Inc. develops powerful Internet technologies, and educational software. is a highly interactive Internet graphics scripting technology. L3 is unique in its exceedingly small footprint and smooth animation. L3 is an excellent tool for both the p rofessional web designer, and for the amateur designer. L3 is also an ideal environment for teaching computer programming in middle-schools, high-schools and colleges. Available on Windows 95/98/NT. Visit the L3 site to learn more, and to download the free fully functional evaluation copy LogoMation is a low-cost, easy to learn computer programming environment, for middle and high schools. Available on Windows and Macintosh. Visit the LogoMation site to learn more, and to download your free evaluation copy.

15. MAGIC SQUARE http://www.magic-square.net/

16. Magic Squares Applet Java source files. http://mathforum.org/alejandre/java/magpuz/MagPuz.html

Magic Squares Applet The Source Files.... MagPuz.java MagCan.java MagControls.java ColorsWindow.java If questions/suggestions, mailto: suzanne@mathforum.org

17. Shin's Magic Square World What I'm saying here is It's Not Impossible!! . Solutions for the 3 types ofmagic square. Other magic square links. Mutsumi Suzuki's magic square Page http://user.chollian.net/~brainstm/MagicSquare.htm

The Perfect Solution For the M A G I C S Q U A R E KOREAN(Çѱ¹¾î·Î) Since July 1997 Yes, you can make all Magic Squares !! Stories History of Magic Square Suzanne Alejandre's Lo Shu Magic Square homepage shows a detail legend of Lo Shu in China. Magic squares have been around for over 3,000 years.. What's a Magic Square? The following definition is a quote from Allan Adler's What is a Magic Square? homepage. A magic square is an arrangement of the numbers from to n^2 (n-squared) in an n x n 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. It is not hard to show that this sum must be n(n^2+1)/2. What I'm saying is.. . When I was young I saw a 3x3 magic square. 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. I started to find out the solution for all numbers. I tried to look for any books written on magic squares, but I could not find a regular solution for n=6,10,14,.. at anywhere. Even somebody said 'It's an unsolved mystery'. But, I found out the principle of constructing squares for other sizes and checked that sums are correct by using a computer. Perhaps a man I don't know has already solved this mystery. I hope that more information and news are exchanged at this site. Anyway, I am content to have solved it by myself. Now, the magic square is no more an unsolved mystery. What I'm saying here is " It's Not Impossible!!

18. Maths Index Articles and images on recreational math from fractals and magic squares to mathemorchids and Galois. http://www.geocities.com/aladgyma/articles/scimaths/maths.htm

Maths Index Sick Sick Six Some simple mathematics associated with 666, the Number of the Beast. Mathemorchids The algorithms of nature. Polygrammagick The lesser-known cousins of magic squares. Koch Doodles Fun with fractal snowflakes. 222 Divine Some interesting facts associated with the second repunit. 111 Chariots The 111 instances of the word "chariots" in the Old Testament of the King James Bible. Dying Jungian Rimbaud vs Galois, or Poetry vs Maths Gamma, Gamma, Gamma, Hey! The swastika and 1/273. Spirals created from the digits of reciprocals. Delete and Repeat till Complete Deletion algorithms and multiplicative palindromes. Reciprocal Arrangements Pseudo-magic squares. Return to Main Articles Index Unless otherwise stated, all articles are by Simon Whitechapel

19. Magic Square closed. http://www.magicsquare.be/

20. Magic Square magic square and five pennies It is divided into two parts; the lower part is a3 by 3 magic square, and the upper part has three numbers 10, 20, and 30. http://www.math.nmsu.edu/breakingaway/Lessons/magicsquare1/magicsquare.html

Magic Square and five pennies Activity Supplies: 3x5 index cards, markers, pencils, rulers, pennies (5 for each child) A magic square is a square array of consecutive natural numbers, 1, 2, 3, ..., such that the sums of the numbers in each row, in each column, and on both diagonals are the same. Creating magic squares is a very ancient art, and the smallest and best known one is Memorizing addition facts, and being able to recall them instantly, is as important now as it ever was. But many methods for teaching addition facts that have been used previously are not acceptable today. One method involving the whole class worked as follows: The teacher says two numbers, for example "seven, six", and points to a student. The student must immediately get up, stand at attention, answer, "thirteen", and sit down. In this way, in a few minutes every student would answer two or three questions, and everyone was paying attention because he or she could be asked to answer the next question. This kind of "military drill" is not acceptable anymore, but achieving almost automatic computation of sums of small numbers requires a large amount of practice distributed over a long period of time, which is quite a boring activity. The magic square board, described below, is designed to provide practice in addition facts which can be done with the whole class under the teacher's direction.

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