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Magic Square
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Includes short description of magic squares. Keeps records for largest hand-written squares between 1975 and 1990.
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The Magic Square Record A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum. Example sum is 15 for each row, column and diagonal) 4 9 2 3 5 7 8 1 6 There...Description, properties and on-line construction. Tour of famous squares. (English/German) [Flash optional]
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Magic Squares It is the oldest known magic square of the world. And you have the possibility to create millions of other, different magic squares online on these pages. These pages use CascadingStyleSheets (CSS) and JavaScript and are optimized for MS Internet-Explorer...Pages on magic squares, stars (original material) and miscellaneous number patterns. Downloads include BASIC programs, Excel and .zip files.
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Magic Squares, Stars, and Other I hope you enjoy these examples from my collection of number patterns. This site has three sections, with pages on magic squares, magic stars (a lot of original material) and miscellaneous number patterns. This site should be of interest to...Introduction to Magic Stars. Construction, analysis and transformations.
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Mutsumi Suzuki: Magic Stars His research interests include reduced gravity and chemical engineering, and process system engineering. Magic Squares are one of his hobbies, of which the magic stars outlined on these pages are an extension Privacy Policy Terms of Use] Home||The Math Library||Quick...Enter numbers and display the magic square in gif or jpg formats.
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Simple Magic Square checker and gif maker Square checker and gif maker by Fabrizio Pivari version 4.3 1997/06/19 Magic square elements (each separated by Default is blank 8 1 6 3 5 7 4 9 2 (Note: you can use letter and negative numbers Functions Skip blanks...Java applet and source files.[JRE to run]
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Magic Squares Applet Morton wrote this applet while participating in the Math Forum's 1996 Summer Institute. Once we cataloged this applet in our Math Tools project, its functionality in different browsers and platforms was raised in a discussion. If this version does not...Includes classroom material covering introduction, the math behind, and methods of construction.
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Math Forum: Allan Adler Multiplying Magic Squares How to construct magic squares Exploring the math Review unit: squaring a magic square What is a magic square Privacy Policy Terms of Use] Home||The Math Library||Quick Reference||Search||Help 1994-2005 The Math Forum http mathforum.org/ Web page design and graphics by...Solve this 4x4 jig-saw puzzle. [Flash]
http://www.dubster.com/math
Curriculum resources, student activities and explanations of puzzles.
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Math Forum: Suzanne Alejandre: Magic Squares Magic squares received their name because there are so many relationships between the sums of the numbers filling the squares. Students often believe that mathematics was written by one person. In these pages you will find that the magic square...How Benjamin Franklin constructed his magic squares. Autobiographical extract included.
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Franklin's Magic Squares Being one day in the country at the house of our common friend, the late learned Mr. Logan, he showed me a folio French book filled with magic squares, wrote, if I forget not, by one M. Frenicle [Bernard Frenicle...Squares that remain magic after entries are raised to various powers. Examples, constructions, bibliography and links compiled by Christian Boyer. (English/French/German)
http://www.multimagie.com/
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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A refreshing new look at a timeless topic, brimming over with ideas, littered with surprising twists. Anyone who loves numbers, anyone who enjoys puzzles, will find The Zen of Magic Squares, Circles, and Stars compulsive (and compulsory reading Ian Stewart,...Presents the "Magic Carpet" approach by "Grog". Downloads available for analyzers and creators in Excel format.
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Redirect You will be automatically redirected in 10 seconds....A 25x25 magic square with 25 sub-squares and other properties. Maple program and PostScript files available for download.
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A very, very Magic Square It has the following properties: Then entries of the square are the numbers 1,2 625=25x25. All its column sums, row sums and both diagonal sums are all equal to 7825=25x(1+625)/2. If the square is divided up in 25 5x5 squares,...Introduction. Prime magic squares, programs and examples.
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Index of prime magic squares What is a prime magic square? Prime Analysis: How is the magic constant for prime magic square and what order are available? Muncey Analysis: How was build the Muncey order 12 magic square? Manual Construction: see how I manually (with...Encyclopedia with articles relating to magic squares, cubes, hypercubes and other objects
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Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube, Tetraspace magic squares and cubes multimagie.com Magic Squares Magic Squares by Grog Number Galaxies Magic Squares Multiplication in a new context Magic Squares and Hypercubes A magic square is a 2-dimensional hypercube every orthogonal square in a hypercube ought to...Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes. (English/Japanese)
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Magic Cubes and Tesseracts What are magic cubes and magic tesseracts? Terms Classes of magic cubes Magic cubes of each order, Magic tesseracts of each order Works on magic cubes, Works on magic tesseracts and hypercubes Algorithms to make magic cubes and tesseracts Theorems...Definition, examples, and construction. Includes algorithms for odd, doubly and singly even squares.
http://mathworld.wolfram.com/MagicSquare.html
Brief history and definition. Construction algorithms are presented for the odd, even, and singly even squares. (English/Korean)
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Shin's Magic Square World Square homepage shows a detail legend of Lo Shu in China. Magic squares have been around for over 3,000 years What's a Magic Square? The following definition is a quote from Allan Adler's What is a Magic Square? homepage. A...Introduction to the Durer magic square. Activities including the magic carpet.
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magic squares at Math Cats: fun, easy, and interactive! But look at the green markings at the top of this page! This special magic square adds up to the same number in all of these ways Don't take our word for it! Use your mental math and see for...Introduction to magic squares. Basic/C computer programs to generate odd squares. Calculates 8x8 squares with any given date on the first line.
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Magic Squares All You Ever Wanted To Know I have often admired the mystical way of Pythagoras, and the secret magic of numbers Sir Thomas Browne, 1605 1682 The above quotation accurately describes my own fascination with numbers generally, but also with Magic Squares (or Quadramagicology, as New...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.
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The Anti-Magic Square Project This web site documents my 1999 summer research on a combinatorial design called the Anti-Magic square. Anti-Magic Squares are a variation on the heavily studied and well-understood magic square. In contrast, very little seems to be known about AMSs. These...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].
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Finding Magic Squares Using CCM N integers of all the columns, all the rows, or a diagonal must be the same. A method of finding a magic square using CCM is explained here. A method of finding a magic square using CCM The applet below...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]
http://www.ouh.nl/open/eyn/applets/magicsq.htm
Introduction with reference to Victor Hill and Bach.
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Ivars Peterson's MathLand: More than Magic Squares I might have employed more usefully I had amused myself in making magic squares. Benjamin Franklin, who made this comment in a letter written more than 200 years ago, was certainly not the first to experience the fascination of magic...An introduction, including computer estimates of squares of different orders.
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Notes on Magic Squares The results of historical and computer enumeration of magic squares All ultramagic squares of order 7 A complete description (10 pages) how all of these squares can be determined. The successful search for the smallest perfect magic cube. How many...Aale de Winkel's site on generalized objects, with generating function f() and conditions g(), sequences and pseudo-rings.
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Generalized Magic Objects ...Visual approach. Definition of Euler and Conway squares, with generating algorithm for the latter via Group Orbits. References.
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Visual Magic Squares and Group Orbits I I am always doing that which I cannot do, in order that I may learn how to do it.”Pablo Picasso Abstract This paper is an essay in visual mathematics that strives to create a guided discovery in which the learner...Definition of nested squares. Generation of even- and odd-sided squares, algorithms and matlab function. Samples of order up to 99 are presented.
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Nested Magic Squares Squares are magic squares with the special property that each sub-magic square within the original square is also magical, i.e the rows, columns, and diagonals add up to the same number (although to a number different than the original sum...The Amazing Mathematical Object Factory generator makes up to 10 squares of order 1 to 10 with just a few clicks. Brief history and introduction included.
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Amof:Info on Magic Squares Now try to place the numbers 1 through 9 into the squares in such a way that all columns, all rows and both diagonals add up to the same amount. The result is known as a magic square. In general,...The Siamese method generates odd squares of any order above one. Explains the mathematics behind the scenes.
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The math behind the Siamese method of generating magic squares Siamese method of generating magic squares What is a magic square A magic square consists of the distinct positive integers 1, 2 n2, such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is...Includes Java Applet and source code of square and hyper cube generator. Options for dimensions and offset.
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Magic Squares and Hyper Cubes Magic squares are arrangements of numbers into squares, cubes, or hyper-cubes where the sum of each row and each column is identical. Additionally, the sum along the principal diagonals is also equal to the same number. The magic square below...A paper describing the generation of 3x3 Distinct Prime Magic Squares using a computer program.
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The 3x3 Distinct Prime Magic Squares Page This page is designed to make available some material on 3x3 distinct prime magic squares, for use by: fans of magic squares and prime numbers, and possibly even serious number theorists. More importantly, this material can be used to introduce...Demonstration of the properties of a pan-magic square.
http://mathworld.wolfram.com/PanmagicSquare.html
Mathematical approach to the generation of order three squares by applying MacMahon's partition analysis.
http://people.brandeis.edu/~maxima/files/papers/magicsquare.pdf
An introduction, with algorithms for generating odd, and doubly even (4k) squares. References.
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Magic Squares An normal magic square is an arrangement of the numbers 1, 2, 3 n2 in a square array, with the property that the sum of every row and column, as well as both diagonals, is the same number. An example...Introduction. World records up to 1994.
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Ulearn Today Magazine Magic squares have been a fascinating area of study in mathematics for centuries and are among the oldest mathematical amusements. What really is a magic square? It's an arrangement of numbers from 1 to n2 in an n x n...Java applet generates odd ordered squares, with options to transformations by rotations and reflections. Souce code provided.
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Magic Squares and Dihedral Group D4 The sum of the numbers in each row, column and main diagonal is the same. It is called the magic constant. In the applet below, magic squares of order (size) 3, 5, 7 and 9 may be explored. A magic...The site presents a program for finding all possible order 3 cubes, executable and source included.
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This program may be used or modified for any non-commercial purpose so long as this original notice remains in place. All other rights are reserved Fill in the numbers 1 through 27 in a 3x3x3 cube so that the sum...An attempt to solve for all possible magic squares, a mathematical treatment.
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Solving Magic Squares Presumably this was not the method used by Bernard Frenicle de Bessy back in 1693 to determine that there are exactly 880 distinct 4x4 magic squares, not counting rotations and reflections Does anyone know what method he actually used There...Presents 2xn and 3xn rectangles, as well as squares of order 4,5 and 8. Generation of the last by knight's tour.
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Magic Rectangles M and each file to the same total N. The totals M and N are termed the magic constants. Since the average value of the numbers is A mn 1)/2, we must have M nA and N mA. The total...Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers. Readers' solutions provided.
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Puzzle 297. Queens on magic squares I will be traveling for the next 15 days through China. If I can get a stable contact with the server of my site from my laptop, I will try to continue posing puzzles, every Saturday morning. Otherwise, the next...The Durer and Loh Shu squares. Starting from basic operations, mathematical derive distinct squares from existing ones.
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Making magic squares This is probably the most famous magic square. It is shown in Drer's woodcut Melancholy and its properties are that each row and each column and both diagonals add to the same sum of 34. This is called the magic...Downloadable program displays random hyper cubes of given order and dimension. It displays simple, pan-n-agonal and perfect hyper-cubes and inlaid squares.
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Hyper Magic Cube This site concerns with the generation of Hyper Magic Cubes, Magic Squares and Magic Rectangles (still working on them) using computer. Since, constructing these figures requires lots of calculations, iterations and deals with large numbers, their combinations, etc. I decided...Demonstrates methods and algorithms for squares and cubes.
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Skeleton Web Squares can be constructed on ANY NUMBER greater than 2 Discover the underlying structures of magic squares and hence how to form such squares. Find out how a4x4square can be made super-magic Extend the use of the `skeleton method to...