Magic Square Recreations Math

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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• 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].
  
• Siamese Method - The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
  
• The 3x3 Distinct Prime Magic Squares Page - A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.
  
• Magic Cubes - Harvey Heinz's introduction to mathematical magic cubes including classification, a time-line and extensive bibliography."
  
• 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.
  
• 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.
  
• 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.
  
• The Magic Square Record - Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
  
• 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.
  
• 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.
  
• MathWorld: Panmagic Square - Demonstration of the properties of a pan-magic square.
  
• Grog's Magic Squares - Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format.
  
• Notes on Magic Squares - Walter Trump explains magic squares, and presents computer estimates of squares of different orders.
  
• Magic Squares by Edward W. Shineman Jr. - Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.
  
• Amof: Information on Magic Squares - The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included.
  
• MathWorld: Magic Squares - Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.
  
• Magic Squares - Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided.
  
• 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 Cubes and Tesseracts - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
  
• Allmath.com: Magic Squares Game - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
  
• Math Forum: Magic Squares Applet - Java applet and source files.[JRE to run]
  
• Making Magic Squares - The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.
  
• 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.
  
• A Very, Very Magic Square - A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
  
• MAA: Ivars Peterson's MathLand: More than Magic Squares - Introduction with reference to Victor Hill and Bach.
  
• Magic Squares at Math Cats: Fun, Easy, and Interactive! - Introduction to the Durer magic square. Activities including the magic carpet.
  
• Math Forum: Multiplying Magic Squares - Includes classroom material covering introduction, the math behind, and methods of construction.
  
• Constructing all Magic Squares of Order Three - Mathematical approach to the generation of order three squares by applying MacMahon's partition analysis. [PDF]
  
• 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.
  
• 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.
  
• 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)
  
• Mathpages: Solving Magic Squares - An attempt to solve for all possible magic squares, a mathematical treatment.
  
• 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.
  
• Math Forum: Magic Stars - Introduction to Magic Stars. Construction, analysis and transformations.
  
• Science News for Kids: MatheMUSEments - Description of Durer's square and an alphamagic square.
  
• The Magic Encyclopedia - Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
  
• Magic Squares and Hyper Cubes - Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.
  
• Magic Square Puzzle - Solve this 4x4 jig-saw puzzle. [Flash]
  
  

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