21. Magic Square -- From MathWorld Similar pages magic square Dancetop PSYCHIC STUNTS, magic square DANCE. by Michael Daniels, http://www.astro.virginia.edu/~eww6n/math/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

22. A Very Magic Square top PSYCHIC STUNTS, A VERY magic square. by Michael Daniels, Your answershould convince you that this is indeed. A VERY magic square. Credits. http://www.mdani.demon.co.uk/stunt/feb97s1.htm

top A VERY MAGIC SQUARE by Michael Daniels The Stunts Quickies Digital Master Test Your ESP! I Ching Oracle Test Your PK! ... The Magic Number 7 A Little Longer ESP Trainer PK Trainer Psi Quiz Experiment An Astrological Mystery ... Poker Challenge At Your Leisure Paranormal Crossword Psychic Safari A Card Prediction A Matter of Intelligence A Very Magic Square Human Levitation Pendulum Power The Spirit Tap Odd Prediction ... Magic Books Consider this Magic Square Note how: The total of every row = The total of every column = The total of both diagonals = The total of the four cells in every corner = The total of the four central cells = The total of the four corner cells = Now do this: Take a sheet of paper about 8-10 inches square. Fold the sheet in half four times so that the folds make a 4 x 4 grid of cells. Open out the sheet and make the folds clear and precise (folding both ways will help).

23. CodeToad - Visual Basic Odd Magic Square . Click Here. Visual Basic Odd magic square. by Thaha Hussain (10/12/2002). Thisarticle is sponsored by FindMyHosting.com. Visual Basic Odd magic square. http://www.codetoad.com/vb_magic_square.asp

CodeToad - Visual Basic Odd Magic Square submit a link privacy contact advertise ... submit your article Search CodeToad Entire site HTML ASP Javascript Java DHTML Visual Basic XML ASP Shopping Cart ASP Forum and more... Web Hosting Search Home Visual Basic Visual Basic Odd Magic Square Article by: Thaha Hussain (10/12/2002) Add to Favourites Tell a friend Sponsored by: Hostway - Your One-Stop Hosing Provider Summary: Magic square is a set of numbers arranged in a particular order whose column-wise, row-wise and diagonal-wise sums are all the same. This program explains the mathematics behind an odd magic square. Magic, Fun, Maths, Interesting, Easy even for beginners and excellent!! Viewed: times Rating (4 votes): out of 5 Rate this Article Read Comments Post Comments Visual Basic Odd Magic Square Magic square is a set of numbers arranged in a particular order whose column-wise, row-wise and diagonal-wise sums are all the same. This program explains the mathematics behind an odd magic square. Magic, Fun, Maths, Interesting, Easy even for beginners and excellent!! To use, simply copy the code below into your VB Project:

24. Index Of Prime Magic Squares Includes an introduction to magic squares, an introduction to prime ones, programs to make magic squares and examples of prime ones. http://digilander.libero.it/ice00/magic/

Index of Prime Magic Squares Index Magic Square: What is a magic square? Prime Magic Square: What is a prime magic square? Prime Analysis: How is the magic constant for prime magic square and what order are available? Muncey Analysis: How was build the Muncey order 12 magic square? Manual Construction: see how I manually (with computer help) construct squares of order 15 and 17. Automatic Construction: see how my programs build (random) prime magic squares of order 12, 15, 17 and 22. Double Square: I build a double square of order 12. See how. Order 35: My program now generate a 35 order prime magic square. Order 124: Yes this high order was generate in semi-automatic mode in a time that I think below of order 35. The order 191 seems near my hand... Muncey Construction: I have suppose the steps used by Muncey to build his 12 order square. Other primes: Here the true prime sequence... All order: Here a riepilogative table for prime magic squares. Speed how fast are the programs?

25. Magic Squares Online construction of magic squares.Category Science Math Recreations magic square......The famous LohShu from 2800 BC It is the oldest known magic squareof the world. And you have the possibility to create millions http://www.magic-squares.de/magic.html

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 Last modified: 01.05.2002

26. The Anti-Magic Square Project The Antimagic square Project. Thanks for your patience and understanding,as this page is still under construction! What is an Anti-magic square? http://www.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:

27. Math Forum: Allan Adler - Multiplying Magic Squares Includes pages, most for use in the classroom, covering What a magic square is, the math behind them and how they are constructed. 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 ... Search http://mathforum.org/ Web page design and graphics by Sarah Seastone

28. Millenium Penny Magic Square In Patagonia At Paso De Indios Contribution to Project Leonardo in Patagonia.There are exactly 2000new coins all dated 2000 in the large magic square. Learning http://www.magicpenny.org/engpennymagicsquare.htm

en Español Home Index / Map Olympics Project Leonardo en Patagonia Contribution of Provincial School 15 Paso de Indios Chubut, Argentina Millenium Penny Magic Square 2000 Information Gallery Photos-Animation Levitation and Mayor of Madryn ... "Imagineering" Exhibition notes- links teachers students, families Can-Coin, Coin-Can Math Frames CoinMath Strips / Mats Coin Darts ... Penny History Children from Dolavon visiting the Millenium Penny Magic Square 2000 at Escuela 15 Paso de Indios. Click photo to enlarge (96K) 2000 December 17 Millenium Penny Magic Square 2000 constructed at Provincial School 15 Paso de Indios. There are exactly 2000 coins, all dated 2000, in the large square. Each of the 16 small squares contains the number of coins shown. Each row, column or diagonal of the large square has a total of 500 coins. Do you agree? The square was built by: Eluney, Emir, Erika, Pamela, Lucas, Ornella and Sofia of our school No. 15, as part of the festivities marking the 64 anniversary of the founding of Paso de Indios. We hope that more permanent Millenium Magic Squares 2000 will be built in open spaces using pebbles instead of coins.

29. Franklin's Magic Squares Covers how Franklin constructed his magic squares including a autobiographical extract and a magic square. http://mathpages.com/home/kmath155.htm

Franklin's Magic Squares Return to MathPages Main Menu

30. Magic Square Of Squares magic square of Squares. It's an open question whether there existsa 3x3 magic square comprised entirely of square integers. Martin http://www.mathpages.com/home/kmath417.htm

Magic Square of Squares Orthomagic Square of Squares Automedian Triangles and Magic Squares Discordance Impedes Square Magic Return to MathPages Main Menu

31. Multimagic Squares magic squares which remain magic after their entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. Site in English and French. http://www.multimagie.com/

32. 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

Hope you like this 3 x 3 Magic square!! Find out more about magic squares. View Benjamin Franklin's 8x8 magic square in animation Poetic Evolution Home Page UNE Page

33. Grog's Magic Squares The Magic Carpet approach to understanding Magic Squares by Grog . http://www.grogono.com/Magic/

Grog's Magic Squares Your Browser does not support FRAMES. We are opening a No Frames version for you

34. Benjamin Franklin's Magic Square There is another animated 8x8 square on the net! I only found theone. Check it out. View my new 3x3 interactive magic square! http://www-personal.une.edu.au/~lgrunwa2/une/KLAs/maths/Benfranklin_magicsquare.

There is another animated 8x8 square on the net! I only found the one. Check it out. View my new interactive Magic Square! Poetic Evolution Home Page UNE Page

35. EvoWeb - Magic Square Flying Circus magic square. Evolution of a magic square. Evolving a magic squareusing Evolution Strategies. Your browser cannot run Java applets. http://evonet.dcs.napier.ac.uk/evoweb/resources/flying_circus/demos/java/demo11.

Whats new Search Site map Browse by subject The online information service for everyone interested in evolutionary computing Resources Membership Working groups Admin You are here: Home page Resources Flying Circus Demos ... Java Magic Square Evolution of a Magic Square. The goal is to arrange the numbers from 1 to N^2 within a NxN grid in such a way that the sum of all rows, the sum of all columns and the sums of both diagonals become equal, i.e. the goal is to find a true magic square. Evolving a magic square using Evolution Strategies Your browser cannot run Java applets. Evolving a magic square using Genetic Algorithms Your browser cannot run Java applets. Chromosome (genotype representation) Evolution Strategy A problem_specific mutation -operator is used. It is based on swapping object-parameters: For each chromosome to be 'mutated' the following process is repeated X times (where X is the strategy_parameters value): A single object parameter is randomly chosen from the n^2 object-parameters. This object parameter is swapped with a second one. The second object parameter is (again) randomly chosen from the n^2 object-parameters, using the restriction that its value must be within a range of +- the first parameters strategy-parameter. All strategy_parameters are equal. The strategy parameters are adapted. With equal probability they are increased by 1, decreased by 1 or kept as they are.

36. EvoWeb - Magic Square Flying Circus magic square. Evolution of a true magic square. This arrangementis called a true magic square. Downloads. Platform Windows MagicSquare.zip. http://evonet.dcs.napier.ac.uk/evoweb/resources/flying_circus/demos/windows/demo

Whats new Search Site map Browse by subject The online information service for everyone interested in evolutionary computing Resources Membership Working groups Admin You are here: Home page Resources Flying Circus Demos ... Windows Magic Square Evolution of a true magic square. On a square grid with n x n fields the numbers from 1 to n x n are initially distributed at random. The aim is to find an arrangement where all sums of columns, all sums of rows and the sums of both the diagonals yield the same value S, the magic sum. This arrangement is called a true magic square. Downloads Platform: Windows MagicSquare.zip Contributed by Michael Herdy Technische Universitaet Berlin Bionik und Evolutionstechnik Email: herdy@fb10.tu-berlin.de WWW: http://lautaro.fb10.tu-berlin.de/user/michael/english/michael.html Full contact info 28 Feb 2003 Email: general contribute feedback EvoWeb is the website of EvoNet - EvoNet is funded by the European Commission's IST Programme

37. LHS Things To Do Item 50 55 of 113 Things to Do magic square MagLev Train Magnetic Drum Makea Maze Make a Motor Go Mandelbrot Set All 113 Things to Do. magic square. http://hueyp.lhs.berkeley.edu/thingstodo/thingstodo.jsp?index=49

38. The Magic Square next up previous Next E 6 Up Exceptional Lie Algebras Previous F 44.3 The magic square. This goes by the name of the `magic square'. http://math.ucr.edu/home/baez/Octonions/node16.html

Next: E Up: Exceptional Lie Algebras Previous: F 4.3 The Magic Square Around 1956, Boris Rosenfeld [ ] had the remarkable idea that just as is the isometry group of the projective plane over the octonions, the exceptional Lie groups and are the isometry groups of projective planes over the following three algebras, respectively: the bioctonions the quateroctonions the octooctonions There is definitely something right about this idea, because one would expect these projective planes to have dimensions 32, 64, and 128, and there indeed do exist compact Riemannian manifolds with these dimensions having and as their isometry groups. The problem is that the bioctonions, quateroctonions and and octooctonions are not division algebras, so it is a nontrivial matter to define projective planes over them! The situation is not so bad for the bioctonions: is a simple Jordan algebra, though not a formally real one, and one can use this to define in a manner modeled after one of the constructions of . Rosenfeld claimed that a similar construction worked for the quateroctonions and octooctonions, but this appears to be false. Among other problems, and do not become Jordan algebras under the product . Scattered throughout the literature [ ] one can find frustrated comments about the lack of a really nice construction of and . One problem is that these spaces do not satisfy the usual axioms for a projective plane. Tits addressed this problem in his theory of `buildings', which allows one to construct a geometry having any desired algebraic group as symmetries [

39. Magic Square Patterns magic square Patterns. The replicated. Square A the 8 patterns generatedfrom rotations and reflections of continuous magic square A. http://web.idirect.com/~recmath/ms04.html

Magic Square Patterns The Javascript Pattern Generator is really the best way to explore the patterns that can be generated from Magic Squares. The following pages give some idea of the kinds of patterns possible. The continuous Magic Squares generate continuous patterns - best seen when the pattern is replicated. Square A the 8 patterns generated from rotations and reflections of continuous Magic Square A Square B the 8 patterns generated from rotations and reflections of continuous Magic Square B Square C the 8 patterns generated from rotations and reflections of continuous Magic Square C All the Patterns all 8 basic patterns (not counting rotations and reflections) Mapping of Squares to Patterns how the three basic squares map to the 8 basic patterns Replicated Pattern P1 the pattern with the most symmetries? Replicated Pattern P2 interesting relationship to a pattern Escher noted in Alhambra tiles Replicated Pattern P3 quilt Replicated Pattern P4 Replicated Pattern P5 Replicated Pattern P6 abstract Replicated Pattern P7 arrows Replicated Pattern P8 Topic Index

40. Magic Square Page 6, 3, 9. magic square Page. I have collected some links to WWW pages on magic squares. NonscalableMethods. A Method for 6x6 Squares. magic square Example Problems. http://www.kanadas.com/puzzles/magic-square.html

Magic Square Page I have collected some links to WWW pages on magic squares. This list includes a link to my page that contains a Java applet that solves magic squares stochastically. This page also contains a link to off-line information Indices Suzanne Alejandre: Magic Squares ``What is a Magic Square?'', History, Mathematics, Geography, ... Magic Squares (Database) by M. Suzuki, including a detailed reference list English Page Japanese Page Magic Square, Cube, Hypercube... Magic Square by Constraint Programming, etc. ``Magic Squares: Filling the Gaps'' Freudenthal-Tits Magic Square Methods of Solving Magic Squares Scalable Methods Solving Magic Squares (a mirror) by CCM its original page by the author of this page Constraint Programming: Magic Squares: Filling the Gaps'' Mixed Integer Programming: Sci.Op-research 1994: MIP formulation of Magic Squares Magic Square: Java applet An Algorithm for odd magic squares Test Nonscalable Methods A Method for 6x6 Squares Magic Square Example Problems by Harvey Heinz Unusual Magic Squares, etc.

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