Magic Square Recreations Math

Magic Square Recreations Math

Magic Square

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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- 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].
- An attempt to solve for all possible magic squares, a mathematical treatment.
- An introduction, including computer estimates of squares of different orders.
- 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.
- Introduction to magic squares, prime magic squares, programs and examples.
- The site presents a program for finding all possible 3x3x3 magic cubes, executable and source included.
- Brief history and definition of magic squares. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean)
- Includes Java Applet generators and source code for magic squares and hyper cubes with options for dimensions and offset.
- Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares.
- Enter numbers and create a magic square in gif or jpg formats.
- Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
- 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]
- The Siamese method generates odd magic squares of any order above one. This site explains in detail the mathematics behind the scenes.
- A magic square puzzle. [Flash]
- Introduction with reference to Victor Hill and Bach.
- Covers how Franklin constructed his magic squares including an autobiographical extract.
- 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.
- A visual approach to the subject. Definition of Euler and Conway squares, with generating algorithm for the latter via Group Orbits. References.
- Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Souce code provided.
- Definition of nested squares. Generation of even- and odd-sided squares, algorithms and matlab function. Samples of order up to 99 are presented.
- Resources for including magic squares in the curriculum, with activities for students and explanations of these interesting puzzles.
- Demonstrates methods and algorithms on how to make magic squares and cubes.
- A concise introduction to the subject, including world records up to 1994.
- Introduction to the Durer magic square. Magic squares activities including the magic carpet.
- 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.
- The "Magic Carpet" approach to understanding Magic Squares by "Grog". Downloads available for analyzers and creators in Excel format.
- Encyclopedia with articles relating to magic squares, magic cubes, magic hypercubes and other objects
- Pages on magic squares, magic stars (a lot of original material) and miscellaneous number patterns. Downloads include BASIC programs, Excel and .zip files.
- A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
- Java applet and source files.[JRE to run]
- 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)
- Description of the Durer's 4x4 Magic Square and an alphamagic square.
- Mathematical approach to the generation of squares of order three by applying MacMahon's partition analysis.
- Introduction to Magic Stars and their construction, analysis and transformation.
- Presents 2xn and 3xn rectangles, as well as squares of order 4,5 and 8. Generation of the last by knight's tour.
- Demonstration of the properties of a pan-magic square.
- Definition, examples, and construction of magic squares, including algorithms for odd, doubly and singly even squares.
- A challenge to put 8 queens on an 8x8 magic square such that the queens sit on prime numbers. Readers' solutions provided.
- History of the Durer and Loh Shu squares. Starting from basic operations, shows how distinct magic squares can be mathematically derived from existing ones.
- Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
- Includes pages, most for use in the classroom, covering what a magic square is, the math behind them and how they are constructed.
- Aale de Winkel's site on generalized magic objects, with generating function f() and magic conditions g(), sequences and pseudo-rings.
- 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.
- Includes short description of a magic square, rules for trying to break a magic square record and all the records between 1975 and now.

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