1. Simple Magic Square Checker And Gif Maker Enter numbers and create a magic square in gif format. 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

2. 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) 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.

3. Education 4 Kids Sponsored By "your Name Here" (a Free Educational Resource) 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 http://www.edu4kids.com/msq

Name: Password: Sponsored by: Your Name Here (contact us for sponsorship) FlashCards Math Square Math Tables Time Experience ... Base Math Grey selection areas are for Members only. Join Now 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

4. Math Forum: Suzanne Alejandre: Magic Squares 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 ... 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

5. Magic Square Take the addition challenge and play the magic square. The objective of the game is to place a number into each square so that the sum of the squares equal to the number on the bottom and to the right of the square. http://www.gomath.com/htdocs/game/magic

Take the addition challenge and play the Magic Square. The objective of the game is to place a number into each square so that the sum of the squares equal to the number on the bottom and to the right of the square. The sum of the numbers you entered must equal to the number on the bottom and to the right of the square when added vertically, horizontally and diagonally. Click on New Game to start playing. Easy Medium Hard Back to GoMath

6. Magic Square, Inc. Founded in 1996, magic square Inc. develops powerful Internet technologies, and educational software. http://www.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.

7. Magic Squares At Math Cats: Fun, Easy, And Interactive! Interactive magic squares! See how many ways the Durer magic square adds up to the same number. Go on to explore other fun magic squares. It is called a "panmagic square." We didn't invent this 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.

8. 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

9. 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 math3@dubster.com for information or try the FAQ

10. Freudenthal-Tits Magic Square FreudenthalTits magic square Here are some approaches from other points of view Geoffrey Dixon. John Baez - Division Algebras. C.H. Barton and A. Sudbery. J. M. Landsberg - Algebraic Geometry. References are based on the Freudenthal-Tits magic square, which shows relationships between division algebras and define the rows of the magic square; Jordan algebras define the columns http://www.innerx.net/personal/tsmith/FTsquare.html

Tony Smith's Home Page Freudenthal-Tits Magic Square: Here are some approaches from other points of view: Geoffrey Dixon John Baez - Division Algebras C.H. Barton and A. Sudbery J. M. Landsberg - Algebraic Geometry ... References The E6-E7-E8 structures are based on the Freudenthal-Tits Magic Square , which shows relationships between division algebras and matrix algebras. In particular: D ivision algebras define the rows of the Magic Square; J ordan algebras define the columns of the Magic Square; and Lie algebras Lie algebras L formed by the rule: L = Der(A) + (A0xJ0) + Der(J) where Der means derivation, + is direct sum, x is tensor product, A0 are the pure imaginary elements of A, R0=S0, C0=S1, Q0=S3, O0=S7, (here Sn means the algebra of tangent vectors to an n-dim sphere, and S0,S1,S3 are Lie algebras Geoffrey Dixon shows how to construct F4, E6, E7, and E8 from a slightly different point of view F4 = Spin(8) + SO(3) + 3x7 = 28 + 3 + 3x7 = 52 E6 = Spin(8) + SU(3) + 6x7 = 28 + 8 + 6x7 = 78 E7 = Spin(8) + Sp(3) + 12x7 = 28 + 21 + 12x7 = 133 E8 = Spin(8) + F4 + 24x7 = 28 + 52 + 24x7 = 248 To get from Geoffrey Dixon's construction to my construction

11. A Very, Very Magic Square Includes a 25x25 magic square, properties of it and Maple and PostScript files for finding more properties of it. 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

12. Magic Squares Math, History, Geography magic squares Math, History, Geography Designed primarily for middle school and older elementary school students, this Math Forum Web unit includes classroom activities for four different squares http://rdre1.inktomi.com/click?u=http://mathforum.org/alejandre/magic.square.htm

13. Math Forum: Allan Adler - What Is A Magic Square? A Math Forum Web Unit Allan Adler s. What is a magic square? The next simplest isthe 3x3 magic square. and those derived from it by symmetries of the square. 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

14. Magic Square -- From MathWorld magic square. If every number in a magic square is subtracted from , anothermagic square is obtained called the complementary magic square. http://mathworld.wolfram.com/MagicSquare.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Algebra Linear Algebra Matrices ... Magic Squares Magic Square A 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 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 n th order general 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).

15. 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:

16. Magic Square From MathWorld magic square from MathWorld A magic square consists of the distinct positive integers 1, 2, , n^2 such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/MagicSquare.html&a

17. 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

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Recreational Mathematics Magic Figures Magic Squares ... magic square with magic constant 34 used in an engraving entitled Melancholia I et al. gnomon magic square Gnomon Magic Square Magic Square search 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

18. Math Forum: Allan Adler - What Is A Magic Square? Multiplying magic squares are techniques developed by Allen Adler and made into Web pages by Sarah Seastone and Suzanne Alejandre. A magic square is an arrangement of the numbers from 1 to n http://mathforum.com/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

19. Magic Squares © dani/19992003. The famous Loh-Shu from 2800 BC It is the oldestknown magic square of the world. And you have the possibility http://www.magic-squares.de/magic.html

url = new Array( 26,0,0, 0,"general/squares/squares.html","Information about magic squares", 0,"general/squares/information.html","Definition of magic squares", 0,"general/squares/magicsum.html","Magic sum", 0,"general/squares/transformations.html","Reflections and rotations of magic squares", 0,"general/squares/count.html","Counting magic squares", 0,"general/squares/number.html","Number of magic squares", 21,0,0, 0,"general/additional/links.html","Links to web sites with magic squares", 0,"general/additional/sitemap.html","Sitemap of www.magic-squares.de" ); The famous Loh-Shu from 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 online on these pages. Comments, Remarks and Questions to Holger Danielsson Letzte Änderung: 26.06.2003

20. Magic Square magic square. Content. Recurring Pattern To Create a magic square by Excel. Magic Circle. Magic Polyhedron http://www.geocities.com/CapeCanaveral/Runway/7228

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