Magic Square
32

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.

### Related categories1

4x4 Magic Square Solver
Given at least two numbers, provides possible solutions for a 4x4 magic square where the desired sum is 34.
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.
Allmath.com: Magic Squares Game
Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
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.
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].
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 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.
The Magic Square Record
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
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 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 with total basic solutions for each order from 5 to 11, and miscellaneous number patterns.
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)
Notes on Magic Squares
Walter Trump explains magic squares, and presents computer estimates of squares of different orders.
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.
Siamese Method
The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
A Very, Very Magic Square
A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
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.
Last update:
August 24, 2016 at 12:05:09 UTC
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