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Science: Math: Recreations: Magic_Square

See also:

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. Magic Squares Game
Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.

Amof: Info on Magic Squares
The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included.

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.

Constructing all Magic Squares of Order Three
Mathematical approach to the generation of order three squares by applying MacMahon's partition analysis. [PDF]

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].

Generalized Magic Objects
Aale de Winkel's site on generalized objects, with generating function f() and conditions g(), sequences and pseudo-rings.

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

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]

MAA: Ivars Peterson's MathLand: More than Magic Squares
Introduction with reference to Victor Hill and Bach.

Magic Cubes
Harvey Heinz's introduction to mathematical magic cubes including classification, a time-line and extensive bibliography."

Magic Cubes
The site presents a program for finding all possible order 3 cubes, executable and source included.

Magic Cubes and Tesseracts
Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)

The Magic Encyclopedia
Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects

Magic Rectangles and Squares
Presents 2xn and 3xn rectangles, as well as squares of order 4,5 and 8. Generation of the last by knight's tour.

Magic Square Puzzle
Solve this 4x4 jig-saw puzzle. [Flash]

The Magic Square Record
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.

Magic Squares
Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided.

Magic Squares
An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.

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

Magic Squares and Hyper Cubes
Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.

Magic Squares at Math Cats: Fun, Easy, and Interactive!
Introduction to the Durer magic square. Activities including the magic carpet.

Magic Squares by Edward W. Shineman Jr.
Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.

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.

Making Magic Squares
The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.

Math Forum: Magic Squares Applet
Java applet and source files.[JRE to run]

Math Forum: Magic Stars
Introduction to Magic Stars. Construction, analysis and transformations.

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.

Mathpages: Solving Magic Squares
An attempt to solve for all possible magic squares, a mathematical treatment.

MathWorld: Magic Squares
Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.

MathWorld: Panmagic Square
Demonstration of the properties of a pan-magic 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)

Nested Magic Squares
Definition of nested squares. Generation of even- and odd-sided squares, algorithms and matlab function. Samples of order up to 99 are presented.

Notes on Magic Squares
Walter Trump explains magic squares, and presents computer estimates of squares of different orders.

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)

Prime Magic Squares
Introduction. Prime magic squares, programs and examples.

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.

Program on Hyper Magic Cubes
Downloadable program displays random hyper cubes of given order and dimension. It displays simple, pan-n-agonal and perfect hyper-cubes and inlaid squares.

Siamese Method
The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.

Simple Magic Square Checker
Enter numbers and display the magic square in gif or jpg formats.

Skeleton Magic Squares
Demonstrates methods and algorithms for squares and cubes.

Ulearn Today : article on Magic Squares
Introduction. World records up to 1994.

A Very, Very Magic Square
A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.

Visual Magic Squares and Group Orbits I
Visual approach. Definition of Euler and Conway squares, with generating algorithm for the latter via Group Orbits. References.

The 3x3 Distinct Prime Magic Squares Page
A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.

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.


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