41. Magic Square - LoveToKnow 1911 Retrieved from http//www.1911encyclopedia.org/magic_square . Categories MAFMAL. Views. Article Discussion what s new Edit History http://www.1911encyclopedia.org/Magic_Square

Magic Square From LoveToKnow 1911 MAGIC SQUARE, a square divided into equal squares, like a chess -board, in each of which is placed one of a series of consecutive numbers from i up to the square of the number of cells in a side, in such a manner that the sum of the numbers in each row or column and in each diagonal is constant. 4 o rob zrr zoo 3 o x 3 z 6 i 6 From a very early period these squares engaged the attention of mathematicians, especially such as possessed a love of the marvellous, or sought to win for themselves a superstitious regard. They were then supposed to possess magical properties, and were worn, as in India at the present day, engraven in metal or stone, as amulets or talismans. According to the old astro logers, relations subsisted between these squares and the planets. In later times such squares ranked only as mathematical curiosities; till at last their mode of construction was systematically investigated. The earliest known writer on the subject was Emanuel Moscopulus, a Greek (4th or 5th century). Bernard Frenicle de Bessy constructed magic squares such that if one or more of the encircling bands of numbers be taken away the remaining central squares are still magical. Subsequently Poignard constructed squares with numbers in arithmetical pro FIG. I.

42. | Magic_Square | Recreations | Math | Science magic_square Recreations Math Science. http://www.smilyx.com/382727/

@import "/s.css"; Add to Favorites Guide Site-Stroy Auto shop Guide Science ... Magic Square Magic Square add +» 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 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 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: 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 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

43. Include Iostream Include Vector Using Namespace Std; Int n ; return 1; } int magic_squareMAX_NMAX_N; for (i = 0; i n; i++) for (j = 0; j n; j++) magic_squareij = square_inputi * n + j; int sum = 0; http://horstmann.com/bigcpp/solutions/ch9/ExP9_23.cpp

#include #include square_input; cout < i < "Sorry; can only process up to " < " by " < n; i++) for (j = 0; j < n; j++) magic_square[i][j] = square_input[i * n + j]; int sum = 0; /* sum up each row */ for (i = 0; i

44. Ruby Quiz - Magic Squares (#124) @magic_square = if (size % 2 != 0) OddMagicSquare.new(size) @magic_squarei,j end These two methods just delegate to the inner square object. http://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:

45. Magic Square An n × n square of the distinct whole numbers 1, 2, , n2, such that the sum of the numbers along any row, column, or main diagonal is the same. http://www.daviddarling.info/encyclopedia/M/magic_square.html

MATHEMATICS A B C ... CONTACT entire Web this site magic square An n n square of the distinct whole numbers 1, 2, ..., n , such that the sum of the numbers along any row, column, or main diagonal is the same. This sum is known as the magic constant and is equal to ½ n n B.C. as lo-shu Each row, column, and main diagonal sums to 15. If the rows are read as three-digit numbers, forwards and backwards, and then squared, we find the interesting relation The reader may wish to see if the same rule holds for the columns and main diagonals. An old Chinese magic square In the early 16th century Cornelius Agrippa constructed squares for n = 3, 4, 5, 6, 7, 8, and 9, which he associated with the seven "planets" then known (including the Sun and the Moon). Albrecht Dürer 's famous engraving of Melancholia (1514) includes a picture of an order-4 magic square. There are 880 distinct squares of order-4 and 275,305,224 squares of order-5, but the number of larger squares is unknown. A square that fails to be magic only because one or both of the main diagonal sums don't equal the magic constant is called a semi-magic square . If all diagonals (including those obtained by wrapping around) of a magic square sum to the magic constant, the square is said to be a

46. Java Programming [Archive] - Arrays And Math.random public class square { public static void main(String args) { int i, j, k; int n, magic_square; magic_square = new int5050; for ( i = 0; i 50; http://forum.java.sun.com/thread.jspa?threadID=543309&messageID=2637121

47. ¹ØÓÚmatlab Builder For JavaµÄʹÓà Translate this page c\\javabuilder_examples\\magic_square\\magicsquare D javabuilder_examples , magic_square. MagicDemoComp http://www.pinggu.org/bbs/Archive_view_71_202277.html

Matlab¼°ÆäËû¼ÆÁ¿Èí¼þר°æ ¹ØÓÚmatlab builder for javaµÄÊ¹Ó ¹ØÓÚmatlab builder for javaµÄÊ¹Ó ´ó¼ÒÓÐÓ¹ýmatlab builder for javaµÄÂð£¿ÎÒ°´ÕÕ°ïÖúÀï±ßµÄÀý×Ó×ö×ÜÊÇÓдíÎ󣬴ó¼ÒÓÐÊÔ¹ýÂð Javaµ÷Ómatlab function,¿É²ÎÕÕjavabuilder.pdf page 1-4 ~ 1-9 Matlab²¿·Ö: 1.Ϊ·½±ã˵÷,ÔÚ´ËÓÚcµú,·Â·¶Àý½¨Á¢×ÊÁϼР2.Encapsulating Your M-Code in a Java Class (page 1-6) 3. Creating a Deployable Client Component (page 1-7) »á²úÉúÁ½¸öfolder : src , distrib Ö÷ÒªÊÇdistribµÄÁ½¸öfile: magicsquare.jar ,magicsquare.ctf Java²¿·Ö: 1.Setting JAVA_HOME on Windows 2.Setting classpath on Windows java getmagic 5 Magic square of order 5 ÎÒÒ²ÏëÓMATLAB Builder for Java ÎÒµÄÊÇmatlab7.0 Àï±ßºÏñ»ÓÐMATLAB Builder for Java ÎÒÏëÎÊÒ»ÏÂÎÒÏëӵĻ°ÐèÒªÖØ×°Ò»¸öеÄmatlab´£¿ »¹ÊÇÖ»ÏÂÒ»¸öMATLAB Builder for Java×é¼þ¾Í¿ÉÒÔÁË £¿ 1.ÎÒÊÇÓMatlab R 2.Javabuilder toolboxÖ÷ÒªµÄ¾ÍÊÇ javabuilder.jar ¼°ËĸöExamples.ÐèÒªµÄ»°ÁôÓÊÏä,ÎҿɼĸøÄã. 3.ÓÉmatlab²úÉú×Ô¼ºÐèÒªµÄxxx.jar,ÓÉÓÚÓÐͼÐνéæ, 4.µ¹ÊÇÒªÓеãjavaµ××Ó,ÒªÉèºpath,classpath,Òª²»È»ºÜÈÝÒ׳ö´í. maner.xiao@gmail.com

48. C++ Translate this page include iostream include iomanip include vector include ctime include cassert include cstdlib using namespace std ; class magic_square http://www.math.ncu.edu.tw/~ziyou/c /practice/load_prac.php?file=magic_square.h

49. Magic Square - Choco The complete code can be found in MagicSquare.java. Retrieved from http//chocosolver.net/index.php?title=magic_square http://choco-solver.net/index.php?title=Magic_square

50. Amazing Squares Brief history and introduction http//glucholazy. info/dmoz/Science/Math/Recreations/magic_square/ Zbiór stron DMOZ - super katalog - magic_square http://www.europex.pl/amazing-squares,10.html

Szukaj: Wyniki amazing squares Recenzja: Six Feet Under (Sześć st³p pod ziemiÄ ) - MuzykaFilmowa O dziwo piosenka " Amazing Life" grupy Jem (Dżem? ;) jest bardzo ładna, klimatyczna i Squares - The Beta Band. 08. Inspiration Information - Shuggie Otis http://www.muzykafilmowa.pl/recenzje/2006/six_feet_under.htm Ten Amazing Fruits 2.1 Trendomierz: Ten Amazing Fruits 2.1. Sudoku Latin Squares Gold 1 » CellFactor: Combat Training Tech Demo vR36 » Ship Simulator 2006 - Titanic Trailer http://www.trendomierz.net/show/216050/ten-amazing-fruits-2-1.html Amazing Slow Downer v2.79 READ NFO by Lz0 Amazing Slow Downer v2.79 READ NFO by Lz0 serial, crack, kod do gry, patche, BF1942 v1.0 [ENGLISH] No-CD Loader Bubbles Squares 1.0 Cam Coder Pro 3.7.4 http://www.allprogramy.pl/Amazing_Slow_Downer_v2.79_READ_NFO_by_Lz0,22808.html Nokia 92xx Communicator software by SymbianWare: Products index They are Lines, Squares and Blocks. Amazing colour graphics, smooth animation and nice sound. Why not to try? But beware it will fascinate you ;-). http://www.symbianware.com/index.php?pl=n9200

51. Ruby Programming Language :: Fwd: Please Forward: Ruby Quiz Submission def magic_square(n) square = .fill(nil,0 n).map{ square = magic_square(n) square.map! { arr arr.map{ x * (digits x.to_s.length) + http://www.megasolutions.net/ruby/Fwd_Please-Forward_Ruby-Quiz-Submission-77935.

Home .Net Programming cSharp Home Sql Server Home ... MS Dynamics CRM 3.0 Ruby Programming Language Fwd: Please Forward: Ruby Quiz Submission Begin forwarded message: - Hide quoted text - @rubyquiz.com, submiss @rubyquiz.com > "Starting from the central column of the first row with the number > wrapped around to the last row or first column, respectively." > puts "+" + ("-" * (n*(digits + 3)-1)) + "+" > puts "+" + ("-" * (n*(digits + 3)-1)) + "+" Begin forwarded message: - Hide quoted text - @rubyquiz.com magic_square.rb Download 124_test.rb Download - Hide quoted text - http://mathworld.wolfram.com/MagicSquare.html for the Begin forwarded message: - Hide quoted text - > From: "Nicolas Modrzyk" <hellon @rubyquiz.com magic_square.rb Download Begin forwarded message: - Hide quoted text - @rubyquiz.com > @plotter = IO.popen(plotter, "w") > @line = "L" > @production = "L+L-L-L+L" > #@production = "L-L+L+L-L+L-L-L+L"

52. !/usr/local/bin/ruby Http//shmach.org As Always, USE THIS CODE @order=order @magic_square=Array.new filling it with nils makes debugging easier @order.times { @magic_square Array.new(@order, nil) } end take where http://shmach.org/downloads/magic_squares.rb

53. Include Iostream Include String Using Namespace Std j; for (i=0;i row;i++) { for (j=0;j col;j++) { cout aTableij ; } cout endl; } } int main() { TwoDimArray magic_square; int i, j, rows, colums; http://www.mpcfaculty.net/tom_rebold/CSIS10B/magic_square_single_file.cpp

#include #include >rows; cout <"Enter a number of colums: "; cin>>colums; for (i=0;i

54. Setuid.net » Tasty Bytes magic_square Enter a nondecimal value to start building the magic square 69 Checking magic square for validity The sum of each row is 651 The sum of http://setuid.net/blog/category/tasty-bytes/

Home In Memoriam Links Contact ... Watch out for that shmmax January 24th, 2008 at 7:34 pm Be sure /proc/sys/kernel/shmmax is set to a large value. echo 134217728 >/proc/sys/kernel/shmmax Add kernel.shmmax = 134217728 to /etc/sysctl.conf so that this parameter is set correctly during the OS boot process. You can set shmmax to larger values but on 32-bit Linux it will wrap around at 4294967296 (4GB). The maximum value for shmmax on 32-bit linux is 4924967295 (4GB - 1 byte). It can also be set to any lower value (134217728, 2147483648, etc) depending on your requirements. You can check this and other shared memory parameters by executing sysctl -a or cat /proc/sys/kernel/shmmax News for Nerds August 24th, 2007 at 9:32 pm I read slashdot Sys Admin Magazine Ceases Publication Testing HTTP via Telnet May 8th, 2007 at 1:46 pm Using telnet to test an HTTP/1.1 request: GET /path/to/some/file HTTP/1.1 ^M HOST: host.domain.tld ^M Connection: close ^M ^M This should generate something like: HTTP/1.1 200 OK Date: Tue, 08 May 2007 17:37:25 GMT

55. Magic Squares (#124) [Ruby] magic_square.rb Magic Square with Odd Number class OddMagicSquare . rick(a)frodo/public/rubyscripts/rubyquiz/trunk/magic_square$ ruby ms_test.rb http://www.adras.com/Magic-Squares-124.t18848-48-1.html

Ruby in [ Ruby Prev: Next: Ruby Libraries From: akbarhome on 20 May 2007 07:52 (a) Here it is: # magic_square.rb # Magic Square with Odd Number class OddMagicSquare attr_reader :square def initialize(n) @square = Array.new(n) middle = n/2 @square[0][middle] = 1 @pos = [0,middle] @len = n end def printing_magic_square v_border = '+' + '-' * (6 * @len - 1) + '+' puts v_border if r then else end end end puts v_border end def iterate_square value = 2 last_value = @len ** 2 while true do move fill value break if value == last_value value = value + 1 end end private def fill(value) @square[@pos[0]][@pos[1]] = value end def move move_down if not move_diagonal_up end def move_diagonal_up # get future position future_pos = Array.new(2) @pos[0] == ? future_pos[0] = @len - 1 : future_pos[0] = @pos[0] @pos[1] == @len - 1 ? future_pos[1] = : future_pos[1] = @pos[1] # check if it is empty or not if @square[future_pos[0]][future_pos[1]] then return false else @pos = future_pos end return true end def move_down @pos[0] == @len - 1 ? @pos[0] = : @pos[0] = @pos[0] + 1

56. > Science> Math> Recreations> Magic Square> Books on magic_square. Music Music on magic_square. Videos Videos on magic_square. See also. Science Math Recreations Games and Puzzles (76) http://www.thelazybastards.com/index.php?browse=/Science/Math/Recreations/Magic_

57. /Science/Math/Recreations/Magic_Square/ : WebPage THAI Open Directory Project : Resource directory for the Internet. /Science/Math/Recreations/magic_square/ Onestop site for all things Internet, large categorized collection of http://search.webpagethai.com/odp/index.php?c=/Science/Math/Recreations/Magic_Sq

58. Porydd Top Science Math Recreations Magic Square. Displaying results 1 10 (of 49) Page 1 2 3 4 5. Thumbnail of http//www.markfarrar. Page 1 2 3 4 5 http://odp.rpfuller.org/porydd/?cat=Science/Math/Recreations/Magic_Square&perpag

59. Magic Square - Wikipedia Magic square. A magic square is an arrangement of numbers in a square grid, in such a way that the sum of the numbers in any row or column gives the same http://facetroughgemstones.com/wikipedia/ma/Magic_square.html

Office Supplies Buy Posters A-Z Products Website Advertising ... Magic square A magic square is an arrangement of numbers in a square grid, in such a way that the sum of the numbers in any row or column gives the same result. Another frequent requirement (satisfied by the above square) is that the only numbers used are 1,2,3,..., n for an n n square. More sophisticated magic squares also produce the sum along the two diagonals; some 4x4 squares also give the sum in any small 2x2 block of four numbers. The 4x4 magic square in Albrecht Dürer 's engraving Melancholia I is believed to be the first seen in European art. The sum 34 can be found in the rows, columns, diagonals, any 2x2 block of numbers, the sum of the four corners, and the sum of the midddle two entries of the two outer columns and rows (eg 5 + 9 + 8 + 12). The two numbers in the middle of the bottom row give the date of the engraving: It has been known since 1693 that there exist 880 basic (excluding those obtained by rotation and reflection) 4x4 magic squares and 275305224 basic 5x5 magic squares. The number of basic magic squares of any higher degreee is not yet known but it was estimated by Klaus Pinn[?]

60. Open Directory - Magic Square - Recreations - Math - Science magic_square. Main Science - Math - Recreations - magic_square. Latest news for this category . magic_square. Site map Site map pages http://odp.toreuse.pl/Science/Math/Recreations/Magic_Square.html

Warning : fopen(cache/Magic Square - Recreations - Math - Science .html) [ function.fopen ]: failed to open stream: No such file or directory in /home/toreuse/public_html/odp/index.php on line Warning /home/toreuse/public_html/odp/index.php on line Warning /home/toreuse/public_html/odp/index.php on line Main Science Math Recreations Latest news for this category: Warning function.curl-setopt ]: CURLOPT_FOLLOWLOCATION cannot be activated when in safe_mode or an open_basedir is set in /home/toreuse/public_html/odp/rss2html.php on line MORE INFO 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. Allmath.com: Magic Squares Game - Interactive game to construct Magic Squares. Different degrees of difficulty and size of square. Hints and solutions provided. 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. 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.

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