Open Directory - Science: Math: Recreations: Magic Square
See also: - Given at least two numbers, provides possible solutions for a 4x4 magic square where the desired sum is 34. - A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download. - Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line. - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided. - The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included. - Includes bordered or consecutively concentric magic squares. Demonstrates odd and even numbered squares and makes bordered squares of any size. - 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]. - Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format. - Introduction with reference to Victor Hill and Bach. - The site presents a program for finding all possible order 3 cubes, executable and source included. - Harvey Heinz's introduction to mathematical magic cubes including classification, a time-line and extensive bibliography." - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese) - Presents 2xn and 3xn rectangles, as well as squares of order 4,5 and 8. Generation of the last by knight's tour. - 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. - Solve this 4x4 jig-saw puzzle. [Flash] - An introduction, with algorithms for generating odd, and doubly even (4k) squares. References. - Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided. - 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. - Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones. - 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. - Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares. - Demonstration of the properties of a pan-magic square. - How Benjamin Franklin constructed his magic squares. Autobiographical extract included. - An attempt to solve for all possible magic squares, a mathematical treatment. - 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 paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program. - 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. - Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects - Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990. - Brief history and definition. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean) - Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares.
