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Science Math Recreations Magic Square
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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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Related categories 1

Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line.
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.
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].
Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
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.
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
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.
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.
A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares.
Pages on magic squares, stars with total basic solutions for each order from 5 to 11, and miscellaneous number patterns.
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.
Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)
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.
Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers. Readers' solutions provided.
Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
Walter Trump explains magic squares, and presents computer estimates of squares of different orders.
The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.
Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
Introduction to the Durer magic square. Activities including the magic carpet.
An attempt to solve for all possible magic squares, a mathematical treatment.
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].
How Benjamin Franklin constructed his magic squares. Autobiographical extract included.
Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.
Introduction. Prime magic squares, programs and examples.
Java applet and source files.[JRE to run]
Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line.
Curriculum resources, student activities and explanations of puzzles.
Demonstration of the properties of a pan-magic square.
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 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
Includes classroom material covering introduction, the math behind, and methods of construction.
Introduction to Magic Stars. Construction, analysis and transformations.
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March 24, 2020 at 6:55:02 UTC
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