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. Magic Square Recreations Math Science.
In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the " magic constant . (wikipedia)
- Wikipedia: In recreational mathematics, a magic square is a square grid filled with distinct numbers such that the numbers in each row, and in each column, as well as the numbers in the main and secondary diagonals, all add up to the same value, called the magic constant. A magic square having n rows is said to be of order n. Thus, a magic square of order n always contains n2 numbers, usually integers. A magic square that contains the integers from 1 to n2 is called a normal magic square.
- Arithmetic sequence - In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
- Combinatorial design - Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
- Freudenthal magic square - In mathematics, the Freudenthal magic square is a construction relating several Lie algebras. It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently.
- John R. Hendricks - John Robert Hendricks was a mathematician specializing in magic squares and hypercubes. He has published many articles in the Journal of Recreational Mathematics as well as other Journals.
- Hexagonal tortoise problem - The hexagonal tortoise problem, a.k.a. jisuguimundo, jisugwimundo was invented by Korean aristocrat and mathematician Seok-jeong Choi, who lived from 1646 to 1715.
- Latin square - In combinatorics and in experimental design, a Latin square is an n n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3x3 Latin square is...
- Magic symbols
- Chinese mathematical discoveries
- Magic squares
- Unsolved problems in mathematics
- Squares Multimagic Squares www
Squares that remain magic after entries are raised to various powers. Squares. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German) Multimagic Squares.
- Brief The Perfect Solutions for the Magic Square www
Brief history and definition. Perfect Solutions for the Magic Square. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean) The Perfect Solutions for the Magic Square.
- Introduction MAA: Ivars Peterson's MathLand: More than Magic Squares www
Introduction with reference to Victor Hill and Bach. MAA: Ivars Peterson's MathLand: More than Magic Squares.
- Java Math Forum: Magic Squares Applet www
Java applet and source files. Forum: Magic Squares Applet.[JRE to run] Math Forum: Magic Squares Applet.
- A A Very, Very Magic Square www
A 25x25 magic square with 25 sub-squares and other properties. Very, Very Magic Square. Maple program and PostScript files available for download. A Very, Very Magic Square.
- An Magic Squares www
An introduction, Squares, with algorithms for generating odd, and doubly even (4k) squares. References. Magic Squares.
- Encyclopedia The Magic Encyclopedia www
Encyclopedia with articles relating to magic squares, Magic Encyclopedia, cubes, hypercubes and other objects The Magic Encyclopedia.
- A The 3x3 Distinct Prime Magic Squares Page www
A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program. The 3x3 Distinct Prime Magic Squares Page.
- Examples, Magic Cubes and Tesseracts www
Examples, Cubes and Tesseracts, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese) Magic Cubes and Tesseracts.
- Try PrimePuzzle #297: Queens on Magic Squares www
Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers. #297: Queens on Magic Squares. Readers' solutions provided. PrimePuzzle #297: Queens on Magic Squares.
- Explores Magic Square Models www
Explores the physical aspects of magic squares. Square Models. 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. Magic Square Models.
- Pages Magic Squares, Magic Stars and Other Patterns www
Pages on magic squares, Squares, Magic Stars and Other Patterns, stars with total basic solutions for each order from 5 to 11, and miscellaneous number patterns. Magic Squares, Magic Stars and Other Patterns.
- The Amof: Information on Magic Squares www
The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Information on Magic Squares. Brief history and introduction included. Amof: Information on Magic Squares.
- The Finding Magic Squares Using CCM www
The Chemical Casting Model (CCM) generation method is demonstrated with a Java Applet. Magic Squares Using CCM. Source code and description of algorithm included. (English/Japanese) [JRE required for Applet only]. Finding Magic Squares Using CCM.
- An Mathpages: Solving Magic Squares www
An attempt to solve for all possible magic squares, Solving Magic Squares, a mathematical treatment. Mathpages: Solving Magic Squares.
- Includes The Magic Square Record www
Includes short description of magic squares. Magic Square Record. Keeps records for largest hand-written squares between 1975 and 1990. The Magic Square Record.
- Starting The Anti-Magic Square Project www
Starting from the definition of an Anti-Magic Square (AMS), Anti-Magic Square Project, the article presents the structure and construction methods of the AMS. Programs written in the c-language are available for download. The Anti-Magic Square Project.
- Features Magic Squares by Edward W. Shineman Jr. www
Features magic squares, Squares by Edward W. Shineman Jr., rectangles and the author's signature magic diamonds commemorating historic and personal milestones. Magic Squares by Edward W. Shineman Jr..
- Includes Math Forum: Multiplying Magic Squares www
Includes classroom material covering introduction, Forum: Multiplying Magic Squares, the math behind, and methods of construction. Math Forum: Multiplying Magic Squares.
- Harvey Magic Cubes www
Harvey Heinz's introduction to mathematical magic cubes including classification, Cubes, a time-line and extensive bibliography." Magic Cubes.
- Java Magic Squares www
Java applet generates odd ordered squares, Squares, with options to transformations by rotations and reflections. Source code provided. Magic Squares.
- The Siamese Method www
The Siamese method generates odd squares of any order above one. Method. Explains the mathematics behind the scenes. Siamese Method.
- Includes Magic Squares and Hyper Cubes www
Includes Java Applet and source code of square and hyper cube generator. Squares and Hyper Cubes. Options for dimensions and offset. Magic Squares and Hyper Cubes.
- Introduction Math Forum: Magic Stars www
Introduction to Magic Stars. Forum: Magic Stars. Construction, analysis and transformations. Math Forum: Magic Stars.
- Solve Magic Square Puzzle www
Solve this 4x4 jig-saw puzzle. Square Puzzle. [Flash] Magic Square Puzzle.
- Interactive Allmath.com: Magic Squares Game www
Interactive game to construct Magic Squares. Magic Squares Game. Different degrees of difficulty and size of square. Hints and solutions provided. Allmath.com: Magic Squares Game.
- Given 4x4 Magic Square Solver www
Given at least two numbers, Magic Square Solver, provides possible solutions for a 4x4 magic square where the desired sum is 34. 4x4 Magic Square Solver.
- Includes Bordered Magic Squares www
Includes bordered or consecutively concentric magic squares. Magic Squares. Demonstrates odd and even numbered squares and makes bordered squares of any size. Bordered Magic Squares.
- Demonstration MathWorld: Panmagic Square www
Demonstration of the properties of a pan-magic square. MathWorld: Panmagic Square.
- The Making Magic Squares www
The Durer and Loh Shu squares. Magic Squares. Starting from basic operations, mathematical derive distinct squares from existing ones. Making Magic Squares.
- How Mathpages: Franklin's Magic Squares www
How Benjamin Franklin constructed his magic squares. Franklin's Magic Squares. Autobiographical extract included. Mathpages: Franklin's Magic Squares.
- Presents Magic Rectangles and Squares www
Presents 2xn and 3xn rectangles, Rectangles and Squares, as well as squares of order 4,5 and 8. Generation of the last by knight's tour. Magic Rectangles and Squares.
- The Magic Cubes www
The site presents a program for finding all possible order 3 cubes, Cubes, executable and source included. Magic Cubes.
- Definition, MathWorld: Magic Squares www
Definition, Magic Squares, examples, and construction. Includes algorithms for odd, doubly and singly even squares. MathWorld: Magic Squares.
- Presents Grog's Magic Squares www
Presents the "Magic Carpet" approach by "Grog". Magic Squares. Downloads available for analyzers and creators in Excel format. Grog's Magic Squares.
- Introduction. Prime Magic Squares www
Introduction. Magic Squares. Prime magic squares, programs and examples. Prime Magic Squares.
- Introduction Magic Squares at Math Cats: Fun, Easy, and Interactive! www
Introduction to the Durer magic square. Squares at Math Cats: Fun, Easy, and Interactive!. Activities including the magic carpet. Magic Squares at Math Cats: Fun, Easy, and Interactive!.
- Introduction All You Wanted to Know About Magic Squares www
Introduction to magic squares. You Wanted to Know About Magic Squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line. All You Wanted to Know About Magic Squares.
- Walter Notes on Magic Squares www
Walter Trump explains magic squares, Magic Squares, and presents computer estimates of squares of different orders. Notes on Magic Squares.
- Curriculum Math Forum: Suzanne Alejandre: Magic Squares www
Curriculum resources, Forum: Suzanne Alejandre: Magic Squares, student activities and explanations of puzzles. Math Forum: Suzanne Alejandre: Magic Squares.
- Features The Zen of Magic Squares, Circles, and Stars www
Features reviews, Zen of Magic Squares, Circles, and Stars, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares. The Zen of Magic Squares, Circles, and Stars.
- A Mathschallenge.net www
A website dedicated to the puzzling world of mathematics, Mathschallenge.net, with a discussion forum. Mathschallenge.net.
- Interactive Creative puzzles www
Interactive puzzle archive with descriptions for puzzle construction and a special children's puzzle page. Creative puzzles.
- A Math in the Movies www
A guide to major motion pictures with scenes of real mathematics. Math in the Movies.
- View Math Forum: Algebra Problem of the Week www
View this week's algebra problem or those of previous weeks. Math Forum: Algebra Problem of the Week.
- Alexa: Magic Square Recreations
Alexa Directory Top Sites: Magic Square Recreations
- DMOZ: Magic Square Recreations
dmoz.org Directory: Magic Square Recreations