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.
Given at least two numbers, provides possible solutions for a 4x4 magic square where the desired sum is 34.
A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line.
Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
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].
The site presents a program for finding all possible order 3 cubes, executable and source included.
Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
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.
An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.
Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided.
Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.
Introduction to the Durer magic square. Activities including the magic carpet.
Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.
Pages on magic squares, stars with total basic solutions for each order from 5 to 11, and miscellaneous number patterns.
The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.
Java applet and source files.[JRE to run]
Introduction to Magic Stars. Construction, analysis and transformations.
Includes classroom material covering introduction, the math behind, and methods of construction.
Curriculum resources, student activities and explanations of puzzles.
How Benjamin Franklin constructed his magic squares. Autobiographical extract included.
An attempt to solve for all possible magic squares, a mathematical treatment.
Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.
Demonstration of the properties of a pan-magic square.
Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)
Walter Trump explains magic squares, and presents computer estimates of squares of different orders.
Introduction. Prime magic squares, programs and examples.
Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers. Readers' solutions provided.
The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
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.
Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
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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