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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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Allmath.com: Magic Squares Game - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided. The Magic Square Record - Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990. Math Forum: Magic Stars - Introduction to Magic Stars. Construction, analysis and transformations. Math Forum: Magic Squares Applet - Java applet and source files.[JRE to run] Math Forum: Multiplying Magic Squares - Includes classroom material covering introduction, the math behind, and methods of construction. Math Forum: Suzanne Alejandre: Magic Squares - Curriculum resources, student activities and explanations of puzzles. Mathpages: Franklin's Magic Squares - How Benjamin Franklin constructed his magic squares. Autobiographical extract included. 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. A Very, Very Magic Square - A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download. Prime Magic Squares - Introduction. Prime magic squares, programs and examples. Magic Cubes and Tesseracts - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese) MathWorld: Magic Squares - Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares. Magic Squares at Math Cats: Fun, Easy, and Interactive! - Introduction to the Durer magic square. Activities including the magic carpet. 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. 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]. Notes on Magic Squares - Walter Trump explains magic squares, and presents computer estimates of squares of different orders. Siamese Method - The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes. Magic Squares and Hyper Cubes - Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset. MathWorld: Panmagic Square - Demonstration of the properties of a pan-magic square. Magic Squares - An introduction, with algorithms for generating odd, and doubly even (4k) squares. References. Magic Squares - Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided. Magic Cubes - The site presents a program for finding all possible order 3 cubes, executable and source included. Mathpages: Solving Magic Squares - An attempt to solve for all possible magic squares, a mathematical treatment. PrimePuzzle #297: Queens on Magic Squares - Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers. Readers' solutions provided. Making Magic Squares - The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones. Magic Squares by Edward W. Shineman Jr. - Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones. The Magic Encyclopedia - Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects 4x4 Magic Square Solver - Given at least two numbers, provides possible solutions for a 4x4 magic square where the desired sum is 34. Magic Square Models - Explores the physical aspects of magic squares. A mass model demonstrates unique properties associated with the moment of inertia for the square. The topographical model looks at water retention patterns in the square. 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) 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. Magic Squares, Magic Stars and Other Patterns - Pages on magic squares, stars with total basic solutions for each order from 5 to 11, and miscellaneous number patterns.
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