Gourt > Science > Math > Recreations > Magic Square
In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n². The term "magic square" is also sometimes used to refer to any of various types of word square.
Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3. The constant sum in every row, column and diagonal is called the magic sum or magic constant, M. The magic constant of a normal magic square depends only on n and has the value
The middle number can be found by
- 15, 34, 65, 111, 175, 260, …
Games and Puzzles :: Recreations
Currently in Apple store, Penn Square - getting the Magic Mouse. :) It really is a beauty.
jammygan (Jeremy Gan) Fri, 06 Nov 2009 23:59:16 -0000
Currently in Apple store, Penn Square - getting the Magic Mouse. :) It really is a beauty.
Tony's Town Square.....ótima opção de restaurante dentro do Magic Kingdom , fácil de conseguir uma reserva e a comida ainda é italiana!!
Dicasdisney (Carlos Constantinov ) Fri, 06 Nov 2009 20:00:33 -0000
Tony's Town Square.....ótima opção de restaurante dentro do Magic Kingdom , fácil de conseguir uma reserva e a comida ainda é italiana!!
"That's not just any square," Langdon said, grinning. That, Ms. Solomon, is a magic square." #langdon
eiserloh (robert eiserloh) Fri, 06 Nov 2009 15:42:46 -0000
"That's not just any square," Langdon said, grinning. That, Ms. Solomon, is a magic square." #langdon
Magic worlds: Tucked away in one of the dingy dead-ends just off Slaveikov Square in Sofia, Magic Worlds is ove.. http://bit.ly/1VILwj
TSEFeatures (TheSofiaEchoFeatures) Fri, 06 Nov 2009 08:20:15 -0000
Magic worlds: Tucked away in one of the dingy dead-ends just off Slaveikov Square in Sofia, Magic Worlds is ove.. http://bit.ly/1VILwj
Orlando Magic Blog: Amway Center Update: The 875000 square foot Amway Center will open in the fall of 2010 and .. http://bit.ly/DsD50
RehabbRiddim (shaun nelson) Fri, 06 Nov 2009 03:08:22 -0000
Orlando Magic Blog: Amway Center Update: The 875000 square foot Amway Center will open in the fall of 2010 and .. http://bit.ly/DsD50
RT @wdwtweets: TIP: You can meet-n-greet Princess Tiana under a gazebo in Magic Kingdom's Liberty Square behind Ye Olde Christmas Shoppe.
Disney_Diva (Heidi) Fri, 06 Nov 2009 01:54:37 -0000
RT @wdwtweets: TIP: You can meet-n-greet Princess Tiana under a gazebo in Magic Kingdom's Liberty Square behind Ye Olde Christmas Shoppe.
A Very, Very Magic Square - A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
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.
Meta Description: [ This is the first of Mark S. Farrar's pages about Magic Squares. ]
Allmath.com: Magic Squares Game - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.
Amof: Info on Magic Squares - The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included.
Constructing all magic squares of order three - Mathematical approach to the generation of order three squares by applying MacMahon's partition analysis.
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].
Generalized Magic Objects - Aale de Winkel's site on generalized objects, with generating function f() and conditions g(), sequences and pseudo-rings.
Grog's Magic Squares - Presents the Magic Carpet approach by Grog. Downloads available for analyzers and creators in Excel format.
Java applet - A documented Java applet that generates 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]
Meta Description: [ Open Universiteit Nederland voor begeleide zelfstudie. Met informatie over de studierichtingen, studiecentra en
de organisatie.
]
MAA: Ivars Peterson's MathLand: More than Magic Squares - Introduction with reference to Victor Hill and Bach.
Magic Cubes - The site presents a program for finding all possible order 3 cubes, executable and source included.
Magic Cubes and Tesseracts - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
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.
Magic Square Puzzle - Solve this 4x4 jig-saw puzzle. [Flash]
Magic Squares - Description, properties and on-line construction. Tour of famous squares. (English/German) [Flash optional]
Magic Squares - An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.
Magic Squares - Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Souce code provided.
Magic Squares and Hyper Cubes - Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.
Magic Squares at Math Cats: Fun, Easy, and Interactive! - Introduction to the Durer magic square. Activities including the magic carpet.
Meta Description: [ Interactive magic squares! See how many ways the Durer magic square adds up to the same number. Go on to explore other fun magic squares. ]
Making magic squares - The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.
Math Forum: Magic Squares Applet - Java applet and source files.[JRE to run]
Math Forum: Magic Stars - Introduction to Magic Stars. Construction, analysis and transformations.
Math Forum: Multiplying Magic Squares - Includes classroom material covering introduction, the math behind, and methods of construction.
Meta Description: [ Multiplying Magic Squares are techniques developed by Allen Adler and made into Web pages by Sarah Seastone and Suzanne Alejandre. ]
Math Forum: Suzanne Alejandre: Magic Squares - Curriculum resources, student activities and explanations of puzzles.
Meta Description: [ Resources for including a variety of magic squares
in the math curriculum, with activities for students and explanations of
these interesting puzzles. ]
Mathpages: Franklin's Magic Squares - How Benjamin Franklin constructed his magic squares. Autobiographical extract included.
Mathpages: Solving Magic Squares - An attempt to solve for all possible magic squares, a mathematical treatment.
MathWorld: Magic Squares - Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.
MathWorld: Panmagic Square - Demonstration of the properties of a pan-magic square.
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)
Meta Description: [ Magic and multimagic squares. Carrés magiques et multimagiques. ]
Nested Magic Squares - Definition of nested squares. Generation of even- and odd-sided squares, algorithms and matlab function. Samples of order up to 99 are presented.
Prime Magic Squares - Introduction. Prime magic squares, programs and examples.
Meta Description: [ Prime Magic Square Research ]
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.
Science News for Kids: MatheMUSEments - Description of Durer's square and an alphamagic square.
Siamese method - The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
Skeleton Magic Squares - Demonstrates methods and algorithms for squares and cubes.
The 3x3 Distinct Prime Magic Squares Page - A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.
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.
The Magic Encyclopedia - Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
The Magic Square Record - Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
Meta Description: [ World Record for the Largest Magic Square ]
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)
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.
500
Ulearn Today : article on Magic Squares - Introduction. World records up to 1994.
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.
Walter Trump: Notes on Magic Squares - An introduction, including computer estimates of squares of different orders.
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