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Magic Square

Science > Math > Recreations > Magic Square

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4x4 Magic Square Solver - http://quasistoic.org/fun/magicsquare/
Given at least two numbers, provides possible solutions for a 4x4 magic square where the desired sum is 34.

A Very, Very Magic Square - http://www.math.lsa.umich.edu/~hderksen/magic.html
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 - http://www.markfarrar.co.uk/msfmsq01.htm
Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line.

Allmath.com: Magic Squares Game - http://www.allmath.com/magicsquare.php
Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.

Amof: Information on Magic Squares - http://theory.cs.uvic.ca/~cos/amof/e_magiI.htm
The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included.

Bordered Magic Squares - http://users.eastlink.ca/~sharrywhite/BorderedMagicSquares.html
Includes bordered or consecutively concentric magic squares. Demonstrates odd and even numbered squares and makes bordered squares of any size.

Finding Magic Squares Using CCM - http://www.kanadas.com/ccm/magic-square/index.html
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].

Grog's Magic Squares - http://www.grogono.com/Magic/
Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format.

MAA: Ivars Peterson's MathLand: More than Magic Squares - http://www.maa.org/mathland/mathland_10_14.html
Introduction with reference to Victor Hill and Bach.

Magic Cubes - http://www.delphiforfun.org/Programs/Source_Listings/MagicCubeSource.html
The site presents a program for finding all possible order 3 cubes, executable and source included.

Magic Cubes - http://members.shaw.ca/hdhcubes/
Harvey Heinz's introduction to mathematical magic cubes including classification, a time-line and extensive bibliography."

Magic Cubes and Tesseracts - http://homepage2.nifty.com/googol/magcube/en/
Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)

Magic Rectangles and Squares - http://www.gpj.connectfree.co.uk/mrm.htm
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 Models - http://www.knechtmagicsquare.paulscomputing.com/
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.

Magic Square Puzzle - http://www.dubster.com/math
Solve this 4x4 jig-saw puzzle. [Flash]

Magic Square: Java applet - http://www.open.ou.nl//eyn/applets/magicsq.htm
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]

Magic Squares - http://www.jcu.edu/math/vignettes/magicsquares.htm
An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.

Magic Squares - http://www.wou.edu/~burtonl/magic.html
Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided.

Magic Squares and Hyper Cubes - http://net.indra.com/~charliek/
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! - http://www.mathcats.com/explore/puzzles/magicsquare.html
Introduction to the Durer magic square. Activities including the magic carpet.

Magic Squares by Edward W. Shineman Jr. - http://www.eds-magic-squares.com
Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.

Making Magic Squares - http://www.netcomuk.co.uk/~jenolive/roymagic.html
The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.

Math Forum: Magic Squares Applet - http://mathforum.org/alejandre/java/magpuz/MagPuz.html
Java applet and source files.[JRE to run]

Math Forum: Magic Stars - http://mathforum.org/alejandre/magic.star/
Introduction to Magic Stars. Construction, analysis and transformations.

Math Forum: Multiplying Magic Squares - http://mathforum.org/alejandre/magic.square/adler/
Includes classroom material covering introduction, the math behind, and methods of construction.

Math Forum: Suzanne Alejandre: Magic Squares - http://mathforum.org/alejandre/magic.square.html
Curriculum resources, student activities and explanations of puzzles.

Mathpages: Franklin's Magic Squares - http://mathpages.com/home/kmath155.htm
How Benjamin Franklin constructed his magic squares. Autobiographical extract included.

Mathpages: Solving Magic Squares - http://www.mathpages.com/home/kmath295.htm
An attempt to solve for all possible magic squares, a mathematical treatment.

MathWorld: Magic Squares - http://mathworld.wolfram.com/MagicSquare.html
Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.

MathWorld: Panmagic Square - http://mathworld.wolfram.com/PanmagicSquare.html
Demonstration of the properties of a pan-magic square.

Multimagic Squares - http://www.multimagie.com/indexengl.htm
Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)

Notes on Magic Squares - http://www.trump.de/magic-squares/index.html
Walter Trump explains magic squares, and presents computer estimates of squares of different orders.

Prime Magic Squares - http://digilander.libero.it/ice00/magic/
Introduction. Prime magic squares, programs and examples.

PrimePuzzle #297: Queens on Magic Squares - http://www.primepuzzles.net/puzzles/puzz_297.htm
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 - http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse1103.asp
Description of Durer's square and an alphamagic square.

Siamese Method - http://www.xs4all.nl/~thospel/siamese.html
The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.

The 3x3 Distinct Prime Magic Squares Page - http://www.dcs.gla.ac.uk/~pd/Numbers/MagicSquares/
A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.

The Magic Encyclopedia - http://www.magichypercubes.com/Encyclopedia/
Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects

The Magic Square Record - http://www.recordholders.org/en/records/magic.html
Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.

The Perfect Solutions for the Magic Square - http://user.chollian.net/~brainstm/MagicSquare.htm
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 - http://sprott.physics.wisc.edu/pickover/zenad.html
Features reviews, information and index of Clifford A. Pickover's book. Publication focuses on historical and cultural attitudes towards the significance of the squares.

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