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         Magic Square:     more books (100)
  1. One Magic Square: The Easy, Organic Way to Grow Your Own Food on a 3-Foot Square by Lolo Houbein, 2010-02-16
  2. Ben Franklin and the Magic Squares (Step-Into-Reading, Step 4) by Frank Murphy, 2001-02-27
  3. Magic Square: Find the solution (Volume 1) by Gregory Zorzos, 2010-06-01
  4. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions by Clifford A. Pickover, 2002-06-15
  5. Square Magic Quilts by Michelle J. Linder, 2009-08-04
  6. Magic Squares by Mark S. Farrar, 2007-01-11
  7. Western Mandalas of Transformation: Magical Squares - Tattwas - Qabalistic Talismans (Llewellyn's Golden Dawn Series) by Soror A.L., 1996-04-08
  8. Before Sudoku: The World of Magic Squares by Seymour S Block, Santiago A Tavares, 2009-02-24
  9. Magic squares and cubes by W S. b. 1847 Andrews, Paul Carus, et all 2010-08-27
  10. Magic Squares: Learning the Inverse Relationships Between Addition and Subtraction (Math for the Real World) by Colleen Adams, 2004-01
  11. The Magic Square: Cities in Ancient China by Arnoldsche Verlagsanstalt Gmbh, 1996-01-25
  12. Occult Encyclopedia of Magic Squares: Planetary Angels and Spirits of Ceremonial Magic by Nineveh Shadrach, 2009-08-20
  13. Magic Squares and Tree of Life: Western Mandalas of Power by Nineveh Shadrach, 2009-05-01
  14. Latin Squares, Volume 46: New Developments in the Theory and Applications (Annals of Discrete Mathematics) by J. Denes, A.D. Keedwell, 1991-02-07

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.
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 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
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.
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.)
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
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

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.
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.
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: Questions and information:

5. - 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.
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 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 and a dvifile magicsqr.dvi of the magic square. 1,
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 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,
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.

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.
Page Patterns and
Magic Squares (1)

Patterns and

Magic Squares (2)

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

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." Rivera, C. "Melancholia."
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
Sponsored by: WellCenter Healthy minds, healthy bodies.
SPECIAL OFFERS from Hooked on Phonics and Scholastic
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. - 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?
Option Explicit 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!
About Welcome!
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Who are We?

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.
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 . Founded in 1996, magic square Inc. developspowerful Internet technologies, and educational software. Visit the L3 site.
general information.... tech support.... marketing.... 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.


16. Magic Squares Applet
Java source files.
Magic Squares Applet
The Source Files....

If questions/suggestions, mailto:

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
The Perfect Solution For the
KOREAN(Çѱ¹¾î·Î) Since July 1997
Yes, you can make all Magic Squares !!
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.
Maths Index
Return to Main Articles Index Unless otherwise stated, all articles are by Simon Whitechapel

19. Magic Square

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.
Magic Square
and five pennies Activity
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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