magic square

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• - Presents 2xn and 3xn rectangles, as well as squares of order 4,5 and 8. Generation of the last by knight's tour.
  
• - Includes short description of a magic square, rules for trying to break a magic square record and all the records between 1975 and now.
  
• - The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10 with just a few clicks. Brief history and introduction included.
  
• - A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.
  
• - A Java applet complete with instructions that creates Magic Squares using a given starting number, increment, and starting location. Row, column and diagonal sums are displayed on request. Odd orders up to 7 are accepted. [JRE required]
  
• - Description of the Durer's 4x4 Magic Square and an alphamagic square.
  
• - Brief history and definition of magic squares. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean)
  
• - History of the Durer and Loh Shu squares. Starting from basic operations, shows how distinct magic squares can be mathematically derived from existing ones.
  
• - A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
  
• - Introduction to the Durer magic square. Magic squares activities including the magic carpet.
  
• - Enter numbers and create a magic square in gif or jpg formats.
  
• - From the Lo-Shu square, the story goes to another apparently simple square that has unusual alphamagic properties. A Pascal program is provided for the curious mind.
  
• - A challenge to put 8 queens on an 8x8 magic square such that the queens sit on prime numbers. Readers' solutions provided.
  
• - The "Magic Carpet" approach to understanding Magic Squares by "Grog". Downloads available for analyzers and creators in Excel format.
  
• - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
  
• - 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.
  
• - An introduction, including computer estimates of squares of different orders.
  
• - Definition, examples, and construction of magic squares, including algorithms for odd, doubly and singly even squares.
  
• - Introduction to magic squares. Basic/C computer programs to generate odd magic squares. Calculates 8x8 magic squares with any given date on the first line.
  
• - Mathematical approach to the generation of squares of order three by applying MacMahon's partition analysis.
  
• - Introduction with reference to Victor Hill and Bach.
  
• - Definition of nested squares. Generation of even- and odd-sided squares, algorithms and matlab function. Samples of order up to 99 are presented.
  
• - Pages on magic squares, magic stars (a lot of original material) and miscellaneous number patterns. Downloads include BASIC programs, Excel and .zip files.
  
• - Demonstrates methods and algorithms on how to make magic squares and cubes.
  
• - Magic squares which remain magic after their entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)
  
• - Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares.
  
• - Covers how Franklin constructed his magic squares including an autobiographical extract.
  
• - A magic square puzzle. [Flash]
  
• - Includes Java Applet generators and source code for magic squares and hyper cubes with options for dimensions and offset.
  
• - Demonstration of the properties of a pan-magic square.
  
• - Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Souce code provided.
  
• - Includes pages, most for use in the classroom, covering what a magic square is, the math behind them and how they are constructed.
  
• - The site presents a program for finding all possible 3x3x3 magic cubes, executable and source included.
  
• - A concise introduction to the subject, including world records up to 1994.
  
• - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
  
• - The Siamese method generates odd magic squares of any order above one. This site explains in detail the mathematics behind the scenes.
  
• - Encyclopedia with articles relating to magic squares, magic cubes, magic hypercubes and other objects
  
• - A visual approach to the subject. Definition of Euler and Conway squares, with generating algorithm for the latter via Group Orbits. References.
  
• - Introduction to Magic Stars and their construction, analysis and transformation.
  
• - Introduction to magic squares, prime magic squares, programs and examples.
  
• - An attempt to solve for all possible magic squares, a mathematical treatment.
  
• - Resources for including magic squares in the curriculum, with activities for students and explanations of these interesting puzzles.
  
• - The Chemical Casting Model (CCM) method is used to create Magic Squares as demonstrated with a Java Applet. Source code and description of computation method included. (English/Japanese) [JRE required for Applet only].
  
• - Java applet and source files.[JRE to run]
  
• - Aale de Winkel's site on generalized magic objects, with generating function f() and magic conditions g(), sequences and pseudo-rings.