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.

More information

### Related categories 1

### Sites 27

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].

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 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.

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.

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)

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.

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.

The Magic Encyclopedia

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

Magic Squares by Edward W. Shineman Jr.

Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.

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.

Making Magic Squares

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

Math Forum: Suzanne Alejandre: Magic Squares

Curriculum resources, student activities and explanations of puzzles.

Magic Squares and Hyper Cubes

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

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.

Prime Magic Squares

Introduction. Prime magic squares, programs and examples.

Math Forum: Magic Squares Applet

Java applet and source files.[JRE to run]

Mathpages: Solving Magic Squares

An attempt to solve for all possible magic squares, a mathematical treatment.

MathWorld: Panmagic Square

Demonstration of the properties of a pan-magic square.

MathWorld: Magic Squares

Definition, examples, and construction. Includes algorithms for odd, doubly and singly even 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.

Magic Squares at Math Cats: Fun, Easy, and Interactive!

Introduction to the Durer magic square. Activities including the magic carpet.

Allmath.com: Magic Squares Game

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

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].

The Magic Square Record

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

Math Forum: Multiplying Magic Squares

Includes classroom material covering introduction, the math behind, and methods of construction.

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.

Mathpages: Franklin's Magic Squares

How Benjamin Franklin constructed his magic squares. Autobiographical extract included.

Math Forum: Magic Stars

Introduction to Magic Stars. Construction, analysis and transformations.