1. The Magic Square Record Includes short description of magic squares. Keeps records for largest handwritten squares between 1975 and 1990. 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) There is no such thing like a record for finding the world's largest magic square. There are well-known algorithms for constructing an arbitrarily large magic square. It is easy to compute very large magic squares. However, the records in this list are for printing or writing magic squares. 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 BOOKS: The Zen of Magic Squares, Circles and Stars Solving Magic Squares 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.

2. Math Forum: Suzanne Alejandre: Magic Squares Resources for including a variety of magic squares in the math curriculum, with activities for students and explanations of these interesting puzzles. 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 ... GEOM ART RY - Ralph Martel Benjamin Franklin's 8x8 Magic Square The World of Benjamin Franklin - the Franklin Institute Classroom Activity Pennsylvania, U.S.A. - Benjamin Franklin's State ... Classroom Activity 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 Updated Magic Square Java Applet by Pavel Safronov and Michael McKelvey Dubi Kaufmann's Magic Square Puzzle H. B. Meyer's

3. Dubster.com - Magic Square Puzzle 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. 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 math3@dubster.com for information or try the FAQ Electric floor heat

4. Math Forum: Allan Adler - Multiplying Magic Squares Multiplying magic squares are techniques developed by Allen Adler and made into Web pages by Sarah Seastone and Suzanne Alejandre. http://mathforum.org/alejandre/magic.square/adler/

A Math Forum Web Unit Allan Adler's Multiplying Magic Squares Suzanne Alejandre's Magic Squares About Allan Adler Classroom activities How to construct magic squares ... Help http://mathforum.org/ Web page design and graphics by Sarah Seastone

5. 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

6. Magic Squares At Math Cats: Fun, Easy, And Interactive! Introduction to the Durer magic square. Activities including the magic carpet. http://www.mathcats.com/explore/puzzles/magicsquare.html

contents math cats explore Magic Squares In magic squares, each row and each column and each diagonal adds up to the same number. But look at the green markings at the top of this page! This special magic square adds up to the same number in all of these ways. (Don't take our word for it! Use your mental math and see for yourself!) It is called a "pan-magic square." We didn't invent this magic square. A famous German artist, Albrecht Dürer, included it in an engraving called "Melancholia" in the year 1514! The most magic thing of all is that you can see the year "1514" in the middle of the bottom row. Pass your mouse over the square to see what it looked like in the 1514 engraving! Click on the square to visit our Math Cats' magic square activities.

7. Allmath.com - Magic Squares Game Interactive game to construct magic squares. Different degrees of difficulty and size of square. Hints and solutions provided. http://www.allmath.com/magicsquare.php

Option Explicit Online Dictionary 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 ... Other Math Links Ask The Experts Visit Dr. Math 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.

8. Shin's Magic Square World Brief history and definition. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean) 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!!

9. Magic Squares - All You Ever Wanted To Know This is the first of Mark S. Farrar s pages about magic squares. http://www.markfarrar.co.uk/msfmsq01.htm

Magic Squares "I have often admired the mystical way of Pythagoras, and the secret magic of numbers" - Sir Thomas Browne, 1605 - 1682 The above quotation accurately describes my own fascination with numbers generally, but also with Magic Squares (or Quadramagicology , as " New Scientist " magazine recently called it). I hope to show you in these pages some of the many aspects of Magic Squares, and maybe kindle that spark in you too. The information shown on the pages indicated below is mainly taken from my book on Magic Squares, which I wrote as my "entrance examination" to become a Member of The Magic Circle , although other sources have also been used: What Is A Magic Square? History Of Magic Squares Magic Totals Odd Magic Squares ... Online Store Subscribe to magicsquares Powered by uk.groups.yahoo.com Click on this house to return to my Home Page Created: Sunday 28th December, 1997 Contact Me (since 22 May 1999)

10. A Very, Very Magic Square A 25x25 magic square with 25 subsquares and other properties. Maple program and PostScript files available for download. 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

11. Science News For Kids: MatheMUSEments Tutorial on how to play magic square games. Gives historical background and different types of illustrations. http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse1103.asp

Home Article Archive Agriculture Animals ... Next Site 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. Why pack so much number magic into one square? Astrologers in Dürer's time associated different types of magic squares with the planets, which, in turn, were thought to influence health. The brooding man is suffering from Saturn's "saturnine," or gloomy, influence. He hopes Jupiter's "jovial" four-by-four magic square will draw down, or decrease, Saturn's influence. (Of course this is all absolutely nutters, but that's the history of ideas for you.)

12. Visual Magic Squares And Group Orbits I Visual approach. Definition of Euler and Conway squares, with generating algorithm for the latter via Group Orbits. References. http://www.mi.sanu.ac.yu/vismath/pais/pais.html

Visual Magic Squares and Group Orbits I John Pais e-mail ) and Richard Singer e-mail © 2004 by John Pais and Richard Singer “I am always doing that which I cannot do, in order that I may learn how to do it.” Pablo Picasso Abstract This paper is an essay in visual mathematics that strives to create a guided discovery in which the learner constructs his/her own math concepts, first intuitively, exploring, constructing, and counting 4 4 visual magic squares, and second analytically, using numerical representations and group orbits to classify and generate these visual magic squares. Euler and Conway visual magic squares are introduced and used to easily create and identify 528 of the 880 essentially different 4 4 magic squares. Euler items and their sets of complements are used to count Euler squares. Similarity classes of Conway items are introduced to create diagonal types and row types needed to classify, count, and generate Conway squares. In addition, by extending an intuitive math idea naturally constructed in this process, it is shown how Euler, Conway , and NonConway (4 4) magic squares can be generated using the orbits of appropriately chosen finite groups. In particular, it is shown that each of the six types of Conway squares introduced, can be generated by the transitive action of the

13. Making Magic Squares The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones. http://www.netcomuk.co.uk/~jenolive/roymagic.html

Making magic squares Strictly speaking, any magic square should have all these properties except for the last one. So, for example, a 3 x 3 magic square will use the numbers from 1 to 9. I show below a copy of the earliest known magic square, the Chinese Loh-Shu, from about 2800 BC. I've added colour here to make the distinction between the odd and even numbers stand out more clearly. In fact the yellow blobs should be white, being Yang symbols or emblems of heaven, and the red blobs should be black, being Yin symbols or emblems of earth. Now we'll look at 4 x 4 squares in more detail. If we relax the rule about the numbers having to run from 1 to 16 we can vastly increase the possibilities and also see some interesting maths in action. All magic squares obey two fundamental rules. Rule (1) If you multiply every element in a magic square by the same number then the result is also a magic square. Here's an example, showing M M and You can see that the basic structure of the square is maintained and the new magic square has a magic sum of 3 x 34 = 102. Rule (2) If you add two magic squares then the result is also a magic square. I've shown an example of this below, using

14. Magic Squares 2800 B.C. It is the oldest known magic square of the world. And you have the possibility to create millions of other, different magic squares http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. The Anti-Magic Square Project Starting from the definition of an Antimagic square (AMS), the article presents the structure and construction methods of the AMS. http://io.uwinnipeg.ca/~vlinek/jcormie/

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! What is an Anti-Magic Square? 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 Purpose Given this definition, this research project aims to answer some of the following questions:

16. Simple Magic Square Checker And Gif Maker Enter numbers and display the magic square in gif or jpg formats. 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

17. The 3x3 Distinct Prime Magic Squares Page A paper describing the generation of 3x3 Distinct Prime magic squares using a computer program. http://www.dcs.gla.ac.uk/~pd/Numbers/MagicSquares/

The 3x3 Distinct Prime Magic Squares Page This page is designed to make available some material on 3x3 distinct prime magic squares, for use by: fans of magic squares and prime numbers, and possibly even serious number theorists. More importantly, this material can be used to introduce the concept of algorithmic complexity to novices - this page will be updated in June to include such material. What is a 3x3 distinct prime magic square? It's exactly what it sounds like: a collection of 9 distinct prime numbers organised into a 3x3 grid in such a way that all of the rows, columns, and diagonals sum to the same value (which is three times the value at the centre of the grid). Why study 3x3 distinct prime magic squares? That's a good question. I wrote the prime number generator long ago as a coding exercise, and the 3x3 distinct prime magic square generator was written to answer a puzzle in the department newsletter. I was surprised at how many such squares there are, so just left the generator running.... it eats cycles quietly on my workstation and happily churns out new squares. Whether anyone else is interested in these squares isn't clear, but I thought I'd put the material up on the web in case anyone wanted to look at them. The algorithmic content is useful in that it makes a nice example of how vastly improved algorithms can follow from a deeper understanding of a problem. If you are aware of an application of these squares in any problem area, or of interesting mathematical observations concerning these squares, please do let me know. I'm not currently aware of any practical use for them whatsoever!

18. Magic Squares, Stars, And Other Similar web sites. Links to other magic square, Magic Star and recreational mathematics web sites. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Magic Square -- From MathWorld Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares. http://mathworld.wolfram.com/MagicSquare.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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).

20. 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:

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