101. [math/9908039] The Projective Geometry Of Freudenthal's Magic Square by JM Landsberg 1999 - Cited by 46 - Related articles http://arxiv.org/abs/math/9908039

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math new recent NASA ADS 4 blog links ... what is this? Bookmark what is this? Mathematics > Algebraic Geometry Title: Authors: J. M. Landsberg L. Manivel (Submitted on 10 Aug 1999) Abstract: We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations, and interpreting them in terms of composition algebras. In particular, we show how a class of invariant quartic polynomials can be viewed as generalizations of the classical discriminant of a cubic polynomial. Comments: 30 pages, LaTeX2e Subjects: Algebraic Geometry (math.AG) ; Differential Geometry (math.DG); Representation Theory (math.RT) Cite as: arXiv:math/9908039v1 [math.AG] Submission history From: [ view email Tue, 10 Aug 1999 09:52:29 GMT (32kb) Which authors of this paper are endorsers?

102. Magic Square - Brain Boosters Watch this number game do magic Number Math Play Magic Square http://school.discoveryeducation.com/brainboosters/numberplay/magicsquare.html

103. Ivars Peterson's MathTrek: More Than Magic Squares Introduction with reference to Victor Hill and Bach. http://www.maa.org/mathland/mathland_10_14.html

Ivars Peterson's MathTrek October 14, 1996 More than Magic Squares "In my younger days, having once some leisure (which I still think 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 squares. People have been toying with these number patterns for more than 2,000 years. Typically, a magic square consists of a set of integers arranged in the form of a square so that the sum of the numbers in each row, each column, and each diagonal add up to the same total. If the integers are consecutive numbers from 1 to n ^2, the square is said to be of n th order. Here's an example of a magic square of the fourth order, made up of the first 16 integers. The sum of the numbers in each row, column, and diagonal is 34. There are 880 possible magic squares of the fourth order, not counting reflections or rotations of each pattern. One of the most remarkable of these squares is one that dates back to India in the eleventh or twelfth century. Notice that not only the rows, columns, and diagonals add up to 34 but also the corner 2 x 2 subsquares. And there's more! The four corner numbers add up to 34, as do the four numbers in the center. Other subsquares (such as 3 + 10 + 6 + 15) give the same result. It's also possible to find "split" subsquares and "split" diagonals that work: 7 + 2 + 14 + 11, and so on. In fact, there is an astonishing number of different ways to get the sum 34 out of this particular magic square.

104. Energy Research magic square. circle of nine. There is a relationship between this arrangement and the circle magic square rotation step 3. magic square rotation step 4 http://www.alexpetty.com/

Energy Research The online journal of Alexander S. Petty Water as Fuel with Puharich and Meyer September 17th, 2010 The patent may be downloaded from the link below: http://www.singularics.com/docs/patents/puharich_us4394230.pdf 1) some implementation to manage the waveform 2) an isolation transformer 3) an inductor 4) water fuel cell (a capacitor formed from partially insulated nickel plates with water as dielectric) 5) another inductor This waveform is rectified by the aqueous bath  as the polarity of the water increases over time through the operation of the cell. From 1983 until his death in 1998, Meyer was awarded more then 15 patents as he continually improved upon his version of the technology. The clearest patent he filed on the technology may be downloaded here: http://www.singularics.com/docs/patents/meyer_us4936961.pdf 1) some implementation to manage the energization waveform 2) an isolation transformer 3) an inductor 4) water fuel cell (a capacitor formed from 304L stainless steel coaxial tubes with water as dielectric) 5) another inductor Meyer energized his cell with two square wave frequencies;  a higher frequency which was tuned to bring about electrical resonance between the water cell (a capacitor) and the Vss side inductor and a lower square wave frequency used to gate the resonant frequency at regular intervals. The resulting waveform thus is a train of square pulses followed by a constant off-period.

105. Magic Square - Definition And Meaning From Wordnik Magic square A square that contains numbers arranged in equal rows and columns such that the sum of each row, column, and sometimes diagonal is the same. http://www.wordnik.com/words/magic square

Sign up! Sign in Zeitgeist Word of the day ... Random word Username Password ( Forgot? or Using Facebook Connect logs you in to Wordnik whenever you are logged in to Facebook. Not a member yet? Sign up for an account magic square Add to favorites Add to a list Link to this word [x] ... Tweet Definitions Thesaurus Examples Pronunciations Comments (4) magic square in [x] American Heritage Dictionary (2 definitions) –noun A square that contains numbers arranged in equal rows and columns such that the sum of each row, column, and sometimes diagonal is the same. A similar square containing letters in particular arrangements that spell out the same word or words. Wiktionary (2 definitions) –noun (games, palindromes) A palindromic square word arrangement, usually in the form of a magic amulet. Probably the best-known is the 5x5 square consisting of the words ROTAS OPERA TENET AREPO SATOR. An n-by-n arrangement of n2 numbers such that the numbers in each row, in each column and along both diagonals all have the same sum. GNU Webster's 1913 (2 definitions) numbers so disposed in parallel and equal rows in the form of a square, that each row, taken vertically, horizontally, or diagonally, shall give the same sum, the same product, or an harmonical series, according as the numbers taken are in arithmetical, geometrical, or harmonical progression.

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

Information on Magic Squares Description Example History Applications ... Links Description of the Problem Draw a 3 by 3 grid on a piece of paper. 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, a magic square is an n x n matrix of numbers where each row, each column and both diagonals add up to n n The simplest magic square is the 1 by 1. This is simply a 1. There are no 2 by 2 magic squares, but there are for 3 by 3, 4 by 4, 5 by 5, and so on. Example For example, all the magic squares of size 3 by 3 are shown below: Notice that all of these squares can be obtained from the first one through flips and turns (rotations) of the first magic square. AMOF will only generate one of these 8 squares. A Brief History Magic Squares are claimed to go back as far as 2200 BC when the Chinese called them lo-shu. According to legend, the pattern was first revealed on the shell of a turtle that crawled out of the Lo River in the twenty-third century B.C. Here is the lo-shu magic square: The first indication of any mathematical investigation into magic squares was from Cornelius Agrippa. In the early part of the 15th century in Europe, he constructed magic squares from orders 3 to 9. He associated these squares with the planets then known, including the sun and moon.

107. Puzzle 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

Puzzles Puzzle 297. Queens on magic squares Dear friends: 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 puzzle will come the next 15/1/2005. From the bottom of my heart, enjoy this season holydays and receive my very best wishes for the next year, 2005. Thanks for your continuous support participating in this special circle of friends of the prime numbers. Anurag Sahay poses the following puzzle: Construct a magic square n x n (using the numbers 1 to n ) and place n queens only on these cells which contain prime numbers, such that no queen can take any other queen. 1. What is the smallest magic square (n) having solution? 3. Redo the exercises 1 & 2 with one additional condition: " one of the diagonals should also contain prime numbers only "

108. Franklin Squares This simplest of magic square techniques must have been known to Franklin. Continuing in this manner, one obtains a Franklin magic square with all of http://www.pasles.org/Franklin.html

Franklin Squares Click here for the BRAND NEW Franklin Mathematics Page! Here are Ben Franklin's two famous magic squares which (together with their lesser-known counterparts) are discussed in my paper "The Lost Squares of Dr. Franklin," American Mathematical Monthly , June-July 2001. An entirely different approach is described in my new book on Franklin, due out soon! A hint can be found in "A Bent For Magic," Mathematics Magazine , Feb. 2006. Instead of requiring diagonal sums to be constant (as in a fully magic square), Franklin used "bent rows" such as those highlighted below. The construction I will give owes much to the various papers which attempted to decode Franklin's method [Carus 1906, Marder 1940, Chandler 1951, Patel 1991]. However, these approaches were not concerned with his actual motivation for performing each step. The recipe given below includes speculation on why these particular steps were chosen. Abrahams 1994] and does not appear to give any idea of Franklin's original reasoning. It is important to keep in mind that the author of the squares was unschooled in number theory. For simplicity of notation, the 8-square will be our pictorial model, but the procedure outlined here (and its concomitant motivation) applies to any 8

109. SourceForge.net: Magic Square - Project Web Hosting - Open Source Software SourceForge presents the Magic Square project. Magic Square is an open source application. SourceForge provides the world's largest selection of Open Source Software. http://magicsquare.sourceforge.net/

Magic Square : Project Web Hosting - Open Source Software Magic Square Users Download Magic Square files Donate money Project detail and discuss Get support Not what you're looking for? SourceForge.net hosts over 100,000 Open Source projects. You may find what you're looking for by searching our site or using our Software Map You may also want to consider these similarly-categorized projects: Project Information About this project: This is the Magic Square project ("magicsquare") This project was registered on SourceForge.net on Oct 27, 2009, and is described by the project team as follows:

110. Recmath Home Page - Magic Squares, Polyominos, Puzzles And Projection Patterns Includes pages on magic squares and polyomino patterns and contains related java applets. http://www3.sympatico.ca/diharper/

Puzzle Page - Magic Squares, Polyominoes and Projection Patterns These pages contain some Recreational Mathematics (Recmath) material with a focus on pattern and symmetry. The approach is a bit rambling and definitely short on analysis and proof. Hopefully the visual content makes up for some of the other shortcomings. There are currently five sections, the first of which explores patterns generated when the numbers in a magic square are replaced with a set of geometric shapes. The second section looks at patterns associated with polyominoes when information about the way the polyomino's squares are connected is added. The third section contains some projection (perspective) drawings of collections of cubes and also describes the underlying programming tools used to display the drawings on the web page. The fourth section looks at a link between order five magic squares and polyominoes. Some pictures of integers as set constructions are in the fifth section. The old URL for these pages (from a previous ISP) was web.idirect.com/~recmath. Magic Square Patterns - 1 Magic Square Patterns - 2 Polyomino Connections ... Integers as Sets Last Updated on March 31st 2007 Web Counted visits since May 9th 2001:

111. Ruby Quiz - Magic Squares (#124) A magic square of size N is a square with the numbers from 1 to N ** 2 arranged so that each row, column, and the two long diagonals have the same sum. http://www.rubyquiz.com/quiz124.html

Ruby Quiz Magic Squares (#124) A magic square of size N is a square with the numbers from 1 to N ** 2 arranged so that each row, column, and the two long diagonals have the same sum. For example, a magic square for N = 5 could be: In this case the magic sum is 65. All rows, columns, and both diagonals add up to that. This week's Ruby Quiz is to write a program that builds magic squares. To keep the problem easy, I will say that your program only needs to work for odd values of N. Try to keep your runtimes pretty reasonable even for the bigger values of N: $ time ruby magic_square.rb 9 real 0m0.012s user 0m0.006s sys 0m0.006s For extra credit, support even values of N. You don't need to worry about N = 2 though as it is impossible. Quiz Summary I was pleasantly surprised by the number of people that tackled the extra credit this time around. Essentially, there are different algorithms for building magic squares depending on the size of the square. There are in fact three different algorithms: one for odd sizes, one for doubly even (divisible by 4) sizes, and another for singly even (divisible by 2 but not 4) sizes. One solution that did handle all three cases came from David Tran. Let's dive right into how David constructs the squares:

112. Magic Rectangles 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

Classic Mathematical Recreations Magic Rectangles The basic problem is: To arrange the numbers 1 to mn in an array of m ranks and n files so that each rank adds to the same total 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 of all the numbers in the array is mnA = mM = nN. If mn is even mn + 1 is odd and so for M = n(mn + 1)/2 and N = m(mn + 1)/2 to be whole numbers n and m must both be even. On the other hand if mn is odd then m and n must both be odd, by simple arithmetic. Therefore: An odd by even magic rectangle is impossible. When m = n we have a magic square diagonal magic squares. For some values of n it is also possible to construct pandiagonal magic squares in which the shorter diagonals are joined up in pairs to make broken diagonals each with n numbers like the main diagonals and also adding to the magic constant. A rectangle in which only the ranks but not the files, or only the files but not the ranks, add to a constant value are naturally termed semimagic Note: some writers on "magic squares" use the term to mean diagonal magic squares, and they sometimes refer to squares that do not have the diagonals magic as "semimagic". These usages should be avoided since the above definitions are more generally applicable.

113. Magic Square On Vimeo Magic Square. by Duncan Malashock. 2 years ago 2 years ago Fri, Feb 13, 2009 1 35am EST (Eastern Standard Time). More. More. See all Show me http://vimeo.com/3197260

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

M agic Cubes - Introduction Update-6 Feb. 2010 Much more about Compact and Complete. Small order-4 multiply cubes. Frost Whipple model order-9 nasik. First pantriagonal associated order-4? etc. Tesseracts Nov. 2007 All about magic tesseracts. A new site (because of space) consisting of 11 pages. Update-5 May 2007. Magic cuboids, Magic Knight Tours, transform associated to pantriagonal. Also miscellaneous items and links. Cube Timeline Dec. 2006. I expanded the cube timeline that originally appeared on my Magic Cubes - the Road to Perfect page. Then moved it to a separate page. I included a copy of Table of First Cubes (which is on my Summary page. Search this site powered by FreeFind Index to this page Introduction A brief explanation of the rational and history 6 Classes of Cubes Magic cubes may logically be put into 6 classes Index to Magic Cube Pages on this Site A list of the pages with brief table of contents The tests What I looked at when comparing magic cubes Features of this magic cube site: A brief discussion regarding contents Introduction Several years ago John R. Hendricks introduced a coordinated set of definitions for magic cubes. It included a new definition for the ‘perfect’ magic cube, which is applicable for magic hypercubes of any dimension.

115. Multimagie.com : Carrés Multimagiques, Multimagic Squares, Multimagische Quadrat 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/indexengl.htm

Carrés Multimagiques Multimagic Squares - Multimagischen Quadrate Bienvenue sur le site des carrés multimagiques ! Welcome on the multimagic squares site ! Willkommen auf den Seiten der multimagischen Quadrate ! Pour La Science www.multimagie.com : ce site sur les carrés multimagiques utilise des cadres . Pour pouvoir le consulter correctement, votre navigateur doit supporter les cadres. Toutefois, vous pouvez cliquer sur le langage de votre choix (première ligne de cette page) pour accéder au menu principal. RESUME. Ce site est consacré aux carrés magiques et multimagiques records. Le carré le plus multimagique connu est le carré pentamagique (5-multimagique) construit par Christian Boyer et André Viricel en 2001. Ce carré a été homologué en 2002 par le Guinness des Records. www.multimagie.com : this multimagic squares site is using frames . In order to correctly see it, your browser must support frames. However, you can click on the language of your choice (first line of the current page) in order to access at the main menu. SUMMARY. This site is dedicated to magic and multimagic squares records. The most multimagic known square is the pentamagic (5-multimagic) square built in 2001 by Christian Boyer and André Viricel. This square has been homologated in 2002 as an official Guinness World Record holder.

116. Grey Matters: Blog Oct 28, 2010 magic square I ve talked about magic squares quite a bit before, but the variety of ways people develop to present the magic squares never http://headinside.blogspot.com/

Blog Videos Mental Gym Memory Basics ... Affiliate Program NEW: Braaaaaains! What happens when you mix Halloween and math? In this post, Poe meets Pi, a math professor clones himself, and we try a little I of Newton Read More... (Photo: jpstanley Featured Posts: The Secrets of Nim (Series) This is a multi-part series on Nim, a seemingly fair game that you can always win: Part 1 (Single-Pile Nim) Part 2 (Multi-Pile Nim) Part 3 (Multi-Pile Misère Nim) Wrap-Up ... Wise-Guy Nim (Photo: peteykins Featured Posts: Scam School Meets Grey Matters Two suggestions I've submitted to the popular Scam School series have been turned into episodes: Calendar Nim Penney's Game More Scam School Posts... (Image: Scam School Featured Post: Memorized Deck Online Toolbox A memorized deck can be a powerful tool in the magician's arsenal, but actually developing the skill can seem overwhelming. In this post, I've tried to take the fear away from the memorized deck by showing the best FREE tools to help you start, learn, and better understand this powerful tool. Read More...

117. Allmath.com Features free flashcards, a magic square game, biographies of mathematicians, and other resources. http://www.allmath.com/

Online Dictionary allmath.com Allmath Homepage Math Tools Flash Cards!!! Metric Converter Games The Magic Square Reference Pages Math Glossary Math Headlines Multiplication Table Metric Conv. Factors ... Other Math Links Ask The Experts Visit Dr. Math Visit our Dictionary! ALLwords.com About allmath.com Welcome! Who are We? Advertise Contact Us yahooBuzzArticleCategory = "entertainment"; yahooBuzzArticleHeadline = "math for kids"; http://www.allmath.com/ Other Great Math Links! Fun And Games Kid References Kid Resources Math Articles ... Sponsorship Opportunities yahooBuzzArticleCategory = "entertainment"; yahooBuzzArticleHeadline = "math for kids"; http://www.allmath.com/ Allsites LLC allmath.com, mathbook.com and "virtual mathbook" ® are all service marks of Allsites LLC orlando vacations periodic table metric conversion ... mortgage calculator

118. David Yoon www.davidyoon.com/ Cached - SimilarSet - How to make a magic square of SetConstructing a magic square may seem complex at first glance, but in reality anyone can make one by following this simple process http://www.davidyoon.com/

119. Matrices And Magic Squares :: Matrices And Arrays (MATLAB®) This matrix is known as a magic square and was believed by many in Dürer s For the magic square, A(4,2) is 15. So to compute the sum of the elements in http://www.mathworks.com/help/techdoc/learn_matlab/f2-12841.html

Home Select Country Contact Us Store Search Solutions Academia Support User Community ... View documentation for other releases Contents Index Getting Started Introduction Matrices and Arrays Matrices and Magic Squares ... Z Learn more about MATLAB Matrices and Magic Squares About Matrices Entering Matrices sum, transpose, and diag Subscripts ... The magic Function About Matrices updateSectionId("f2-21117"); Back to Top Entering Matrices The best way for you to get started with MATLAB is to learn how to handle matrices. Start MATLAB and follow along with each example. You can enter matrices into MATLAB in several different ways: Enter an explicit list of elements. Load matrices from external data files. Generate matrices using built-in functions. Create matrices with your own functions and save them in files. Separate the elements of a row with blanks or commas. Use a semicolon, , to indicate the end of each row. Surround the entire list of elements with square brackets, A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] MATLAB displays the matrix you just entered: A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 This matrix matches the numbers in the engraving. Once you have entered the matrix, it is automatically remembered in the MATLAB workspace. You can refer to it simply as

120. Curiousmath :: Math Is An Attitude This is one of the best methods used to create a magic square of any order. I think it came from cracking the code for any odd magic square. http://www.curiousmath.com/

@import url("themes/PostNuke/style/style.css"); curiousmath math is an attitude Oct 31, 2010 - 03:42 AM Home page Downloads Web links FAQ Search Main Menu Home Resources Math Topics Forum Submit Math Article The Top Ten ... Downloads Who's Online There are 84 unlogged users and registered users online. You can log-in or register for a user account here Sponsored Links Welcome to CuriousMath.com Want to learn how to quickly square a number that ends in 5? Or how to tell if a number is divisible by 3? Or maybe you'd like to learn how to calculate square roots by hand? That's the kind of fun and fascinating math tricks and trivia you'll find here at CuriousMath.com. To see all the math stuff that's available, click on Math Topics in the left-hand menu. Or search the site using the Search field at the top of the page. (Just type some words and hit Enter.) I also invite you to Register with us and become a CuriousMath.com member. It's safe, it's free, and it's very cool. Registering allows you to... post comments to the site post messages in the forum send and receive private messages to other members receive occasional emails regarding CuriousMath.com updates

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