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A Magic Square of order n is an arrangement of the numbers from 1 to n^2 (n-squared) in an n by n matrix. The sum of any row, any column, or any main diagonal must be the same. The smallest non-trivial case is of order 3. The same idea can be extended to other shapes such as stars, cubes, circles, and so on. These are called Magic objects.

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Science » Math » Recreations » Games and Puzzles (88)

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Magic Squares Description, properties and on-line construction. Tour of famous squares. (English/German) [Flash optional] www.magic-squares.de/magic.html

Math Forum: Multiplying Magic Squares Includes classroom material covering introduction, the math behind, and methods of construction. mathforum.org/alejandre/magic.square/adler

The Magic Square Record Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990. www.recordholders.org/en/records/magic.html

Magic Squares, Magic Stars and Other Patterns Pages on magic squares, stars (original material) and miscellaneous number patterns. Downloads include BASIC programs, Excel and .zip files. www.geocities.com/~harveyh

Simple Magic Square Checker Enter numbers and display the magic square in gif or jpg formats. www.geocities.com/CapeCanaveral/Lab/3469/squaremaker.html

Magic Square Puzzle Solve this 4x4 jig-saw puzzle. [Flash] www.dubster.com/math

Math Forum: Suzanne Alejandre: Magic Squares Curriculum resources, student activities and explanations of puzzles. mathforum.org/alejandre/magic.square.html

Math Forum: Magic Stars Introduction to Magic Stars. Construction, analysis and transformations. mathforum.org/alejandre/magic.star

Math Forum: Magic Squares Applet Java applet and source files.[JRE to run] mathforum.org/alejandre/java/magpuz/MagPuz.html

Mathpages: Franklin's Magic Squares How Benjamin Franklin constructed his magic squares. Autobiographical extract included. mathpages.com/home/kmath155.htm

Multimagic Squares Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German) www.multimagie.com

The Zen of Magic Squares, Circles, and Stars Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares. sprott.physics.wisc.edu/pickover/zenad.html

Grog's Magic Squares Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format. www.grogono.com/Magic

A Very, Very Magic Square A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download. www.math.lsa.umich.edu/~hderksen/magic.html

Prime Magic Squares Introduction. Prime magic squares, programs and examples. digilander.libero.it/ice00/magic

The Magic Encyclopedia Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects home.wanadoo.nl/aaledewinkel/Encyclopedia

Magic Cubes and Tesseracts Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese) homepage2.nifty.com/googol/magcube/en

MathWorld: Magic Squares Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares. mathworld.wolfram.com/MagicSquare.html

The Perfect Solutions for the Magic Square Brief history and definition. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean) user.chollian.net/~brainstm/MagicSquare.htm

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

All You Wanted to Know About Magic Squares Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line. www.markfarrar.co.uk/msfmsq01.htm

The Anti-Magic Square Project Starting from the definition of an Anti-Magic Square (AMS), the article presents the structure and construction methods of the AMS. Programs written in the c-language are available for download. io.uwinnipeg.ca/~vlinek/jcormie

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

Finding Magic Squares Using CCM The Chemical Casting Model (CCM) generation method is demonstrated with a Java Applet. Source code and description of algorithm included. (English/Japanese) [JRE required for Applet only]. www.kanadas.com/ccm/magic-square/index.html

Java applet A documented Java applet that generates Magic Squares using a given starting number, increment, and starting location. Row, column and diagonal sums are displayed on request. Odd orders up to 7 are accepted. [JRE required] www.ouh.nl/open/eyn/applets/magicsq.htm

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