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 Science > Math > Recreations > Magic Square

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Science > Math > Recreations > Magic Square

Magic Square:

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.

http://www.markfarrar.co.uk/msfmsq01.htm

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Allmath.com: Magic Squares Game

Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided.

http://www.allmath.com/magicsquare.php

Amof: Information on Magic Squares

The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10. Brief history and introduction included.

http://theory.cs.uvic.ca/~cos/amof/e_magiI.htm

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.

http://io.uwinnipeg.ca/~vlinek/jcormie/

Constructing all Magic Squares of Order Three

Mathematical approach to the generation of order three squares by applying MacMahon's partition analysis. [PDF]

http://people.brandeis.edu/~maxima/files/papers/magicsquare.pdf

Design your Magic Square

Enter numbers and display the magic square in gif or jpg formats.

http://www.pivari.com/squaremaker.html

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].

http://www.kanadas.com/ccm/magic-square/index.html

Generalized Magic Objects

Aale de Winkel's site on generalized objects, with generating function f() and conditions g(), sequences and pseudo-rings.

http://home.wanadoo.nl/aaledewinkel/Gen_Magic/

Grog's Magic Squares

Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format.

http://www.grogono.com/Magic/

MAA: Ivars Peterson's MathLand: More than Magic Squares

Introduction with reference to Victor Hill and Bach.

http://www.maa.org/mathland/mathland_10_14.html

Magic Cubes

Harvey Heinz's introduction to mathematical magic cubes including classification, a time-line and extensive bibliography."

http://members.shaw.ca/hdhcubes/

Magic Cubes

The site presents a program for finding all possible order 3 cubes, executable and source included.

http://www.delphiforfun.org/Programs/Source_Listings/MagicCubeSource.html

Magic Cubes and Tesseracts

Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)

http://homepage2.nifty.com/googol/magcube/en/

The Magic Encyclopedia

Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects

http://www.magichypercubes.com/Encyclopedia/

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.

http://www.gpj.connectfree.co.uk/mrm.htm

Magic Square

Solve this 4x4 jig-saw puzzle. [Flash]

http://www.dubster.com/math

The Magic Square Record

Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.

http://www.recordholders.org/en/records/magic.html

Magic Squares

Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Source code provided.

http://www.wou.edu/~burtonl/magic.html

Magic Squares

An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.

http://www.jcu.edu/math/vignettes/magicsquares.htm

Magic Squares and Hyper Cubes

Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.

http://net.indra.com/~charliek/

Magic Squares at Math Cats: Fun, Easy, and Interactive!

Introduction to the Durer magic square. Activities including the magic carpet.

http://www.mathcats.com/explore/puzzles/magicsquare.html

Magic Squares by Edward W. Shineman Jr.

Features magic squares, rectangles and the author's signature magic diamonds commemorating historic and personal milestones.

http://www.eds-magic-squares.com

Magic Squares, Magic Stars and Other Patterns

Pages on magic squares, stars (original material) and miscellaneous number patterns. Downloads include BASIC programs, Excel and .zip files.

http://www.geocities.com/~harveyh/

Making Magic Squares

The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.

http://www.netcomuk.co.uk/~jenolive/roymagic.html

Math Forum: Magic Squares Applet

Java applet and source files.[JRE to run]

http://mathforum.org/alejandre/java/magpuz/MagPuz.html

Math Forum: Magic Stars

Introduction to Magic Stars. Construction, analysis and transformations.

http://mathforum.org/alejandre/magic.star/

Math Forum: Multiplying Magic Squares

Includes classroom material covering introduction, the math behind, and methods of construction.

http://mathforum.org/alejandre/magic.square/adler/

Math Forum: Suzanne Alejandre: Magic Squares

Curriculum resources, student activities and explanations of puzzles.

http://mathforum.org/alejandre/magic.square.html

Mathpages: Franklin's Magic Squares

How Benjamin Franklin constructed his magic squares. Autobiographical extract included.

http://mathpages.com/home/kmath155.htm

Mathpages: Solving Magic Squares

An attempt to solve for all possible magic squares, a mathematical treatment.

http://www.mathpages.com/home/kmath295.htm

MathWorld: Magic Squares

Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.

http://mathworld.wolfram.com/MagicSquare.html

MathWorld: Panmagic Square

Demonstration of the properties of a pan-magic square.

http://mathworld.wolfram.com/PanmagicSquare.html

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)

http://cboyer.club.fr/multimagie/

Notes on Magic Squares

Walter Trump explains magic squares, and presents computer estimates of squares of different orders.

http://www.trump.de/magic-squares/index.html

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)

http://user.chollian.net/~brainstm/MagicSquare.htm

Prime Magic Squares

Introduction. Prime magic squares, programs and examples.

http://digilander.libero.it/ice00/magic/

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.

http://www.primepuzzles.net/puzzles/puzz_297.htm

Program on Hyper Magic Cubes

Downloadable program displays random hyper cubes of given order and dimension. It displays simple, pan-n-agonal and perfect hyper-cubes and inlaid squares.

http://www.geocities.com/soni_abhinav/index.html

Science News for Kids: MatheMUSEments

Description of Durer's square and an alphamagic square.

http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse1103.asp

Siamese Method

The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.

http://www.xs4all.nl/~thospel/siamese.html

A Very, Very Magic Square

A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.

http://www.math.lsa.umich.edu/~hderksen/magic.html

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.

http://www.mi.sanu.ac.yu/vismath/pais/pais.html

The 3x3 Distinct Prime Magic Squares Page

A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.

http://www.dcs.gla.ac.uk/~pd/Numbers/MagicSquares/

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.

http://sprott.physics.wisc.edu/pickover/zenad.html