41. Magic Square - C / C++ Answers magic square. Ask C / C++ questions and get answers from our community of C / C++ experts and professionals on BYTES. http://bytes.com/topic/c/answers/743565-magic-square

/** * vBulletin 3.7.6 CSS * Style: 'bytes.answers'; Style ID: 18 */ @import url("/clientscript/vbulletin_css/style-94eb1e9e-00018.css"); All Topics Business Careers and Education Consulting ... login new member: Register member login: Email Address: Password: lost password? bytes c / c++ c / c++ questions magic square Join Date: Oct 2007 Posts: 11 : Dec 1 '07 Hi, I am working in a program caals magic square and it must be done only with loops and user definied funcations,I will tell you about my code and where my problem, the main is only calls the other funcations,The first funcation makes a squence which the user input where it begins and the differents between easch elements the size of this one dimensional array is 16. the second funcation puts the elements of the one dimensional arry into a two dimensional size 4*4.funcation 3 only print, funcation 4 reverses both the diagonals, funcation 5 which I had a problem with it is that takes the one dimensional array and output it's sum but my problem it only takes the sum of the last four elements and it addes them 16 time, of course the program is not finished because the sum of the one dimensional array divided by four is the magic number,and then I must cheak the sum of the rows and columns to see if itis equal to the magic number.here is my code. Expand Select Wrap Line Numbers using namespace std;

42. 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

by Walter Trump There are more magic squares of order 10 than elementary particles in our universe and in trillions of other universes (if they exist). Number of magic squares The results of historical and computer enumeration of magic squares Ultramagic squares are both pandiagonal and centrally symmetrical. Ultramagic squares of order 7 Properties, transformations and beautiful examples of these squares. Read how to determine all 20,190,684 different squares. Magic series (new formulae discovered!) Read all about these building blocks of magic objects. Don't be afraid of exact numbers with more than 100 digits. How many magic squares of higher orders are there? Estimates of the number of magic squares (cubes, hypercubes) Magic series and probability considerations enable us to estimate the numbers of magic objects. How many magic lines can a magic cube of small order possess? Perfect magic cubes The successful search for the smallest perfect magic cube in 2003. Strategy and source code of a special approximation Number of normal magic order-6 squares Learn about the Monte Carlo backtracking algorithm.

43. Magic Squares - All You Ever Wanted To Know Magic Squares Picture that rotates between a 3 x 3 Magic Square, a 4 x Magic Squares What Is A Magic Square? History Of Magic Squares Magic Totals http://www.markfarrar.co.uk/msfmsq01.htm

Magic Squares "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 Scientist " magazine recently called it). I hope to show you in these pages some of the many aspects of Magic Squares, and maybe kindle that spark in you too. As opposed to other ways people find to spend their time online, such as flash games, bingo , or facebook, Magic Squares are not only fun, but they actually help develop your thinking skills in several different ways (e.g. a Magic Squares worksheet is a great educational puzzle for children - did you know you can even teach your baby math The information shown on the pages indicated below is mainly taken from my book on Magic Squares , which I wrote as my "entrance examination" to become a Member of The Magic Circle , although other sources have also been used: What Is A Magic Square? History Of Magic Squares Magic Totals Odd Magic Squares ... Online Store Magic Squares also present an opportunity to learn about probability theory (e.g. combinations and permutations), which crop up all over the place, including, for example, in working out the number of possible poker hands This is, however, an aspect of Magic Squares that is under-developed by most magicians, who often only highlight a small portion of the truly amazing properties of even small squares, such as the 4 x 4.

44. 4 X 4 Magic Squares This page by Mark Farrar is about 4 x 4 Magic Squares. The 4 x 4 Magic Square to the left is the basic 4 x 4 Magic Square. It uses the numbers 1 to 16 inclusive, and its Magic http://www.markfarrar.co.uk/msq4x401.htm

45. Magic Square, Inc. L3 is a new highly interactive Internet graphics scripting technology. L3 is unique in its exceedingly small footprint and smooth animation. LogoMation is an easy to learn http://www.magicsquare.com/

Founded in 1996, Magic Square Inc. develops powerful Internet technologies, and educational software. is a highly interactive Internet graphics scripting technology. L3 is unique in its exceedingly small footprint and smooth animation. L3 is an excellent tool for both the p rofessional web designer, and for the amateur designer. L3 is also an ideal environment for teaching computer programming in middle-schools, high-schools and colleges. Available on Windows 95/98/NT. Visit the L3 site to learn more, and to download the free fully functional evaluation copy LogoMation is a low-cost, easy to learn computer programming environment, for middle and high schools. Available on Windows and Macintosh. Visit the LogoMation site to learn more, and to download your free evaluation copy.

46. Magic Squares Magic Squares. Quickie Introduction . A curious arrangement of numbers includes what is referred to as a “magic square”. The magic derives from the fact that numbers arranged in a http://www.halexandria.org/dward090.htm

Magic Squares Quickie Introduction A curious arrangement of numbers includes what is referred to as a �magic square�. The magic derives from the fact that numbers arranged in a square of equal sides all add to the same total, coming and going, up and down, and oft times even from an angle (diagonal). For example: Note that the total always adds to 15 (row, column or diagonal), the diagonals no longer necessarily add properly if either the row and/or columns are mixed, and the total of any three rows or columns is 45. This is a magic square of rank 3. More information on this topic can be found at the Halexandria Forums One can also do a 4x4 magic square, e.g. Here the rows and columns add to 34, but in this particular case the diagonals do not. The 3x3 example above is considered Panmagic Diabolical, Nasik, or Pandiagonal , while the 4x4 above is merely magic. It is also possible to start with zero, instead of one, so that a possible 5x5 magic square is: http://www.grogono.com Included is a very brief, traditional history, which notes that �all magic squares have at least eight variations: the square can be rotated into four positions and each of these rotations can be reflected - for a total of eight variations of any one unique design. Most magic squares do not remain magic if one border is moved to the opposite edge - the change leaves the main diagonal no longer magic.

47. 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

The Largest Magic Square 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) There is no such thing like a record for finding the world's largest magic square. There are well-known algorithms for constructing an arbitrarily large magic square. It is easy to compute very large magic squares. However, the records in this list are for printing or writing magic squares. You can read more about magic squares at forum.swarthmore.edu/alejandre/magic.square.html Interesting records for multi-magic squares (not only the sum of the numbers but also the sum of their squares, cubes, etc. must be the same) can be found at www.multimagie.com The Games and Puzzles Journal and the web site magictour.free.fr list interesting Magic Knight Tour records. BOOKS: The Zen of Magic Squares, Circles and Stars Solving Magic Squares The Rules The magic square must be written/printed on paper. It is not sufficient just to calculate it by a computer. It is allowed to compose the magic square from many sheets of paper, but they MUST lay together to form one scheme of numbers. This scheme must be a square, not just any rectangle.

48. Magic Square: Definition From Answers.com n. 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 http://www.answers.com/topic/magic-square

49. Magic Square - Definition And More From The Free Merriam-Webster Dictionary Definition of word from the MerriamWebster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. http://www.merriam-webster.com/dictionary/magic square

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

A Math Forum Web Unit Allan Adler's Multiplying Magic Squares Suzanne Alejandre's Magic Squares About Allan Adler Classroom activities How to construct magic squares ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies Web page design and graphics by Sarah Seastone

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

Franklin's Magic Squares Return to MathPages Main Menu

52. Flickr: Magic Square Magic Square Group Pool Discussion 91 Members Map Join This Group. Group Pool 443 items Only members can add to the pool. Join? http://www.flickr.com/groups/magic-square/

YAHOO.util.Event.addListener(window, 'load', F._window_onload); YAHOO.util.Event.addListener(window, 'resize', F._window_onresize); YAHOO.util.Event.addListener(window, 'blur', F._window_onblur); YAHOO.util.Event.addListener(window, 'focus', F._window_onfocus); YAHOO.util.Event.addListener(window, 'unload', F._window_onunload); You aren't signed in Sign In Help Home The Tour ... This Group's Discussions Magic Square Group Pool Discussion 91 Members Map ... Join This Group Guest Passes let you share your photos that aren't public. Anyone can see your public photos anytime, whether they're a Flickr member or not. But! If you want to share photos marked as friends, family or private, use a Guest Pass. If you're sharing photos from a set, you can create a Guest Pass that includes any of your photos marked as friends, family, or private. If you're sharing your entire photostream, you can create a Guest Pass that includes photos marked as friends or family (but not your private photos). Learn more about Guest Passes!

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

Community Aggiungi lista preferiti Aggiungi lista nera Invia ad un amico Crea Profilo Blog Video Sito Foto Amici Esplora Index of Prime Magic Squares Index Magic Square: What is a magic square? Prime Magic Square: 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 computer help) construct squares of order 15 and 17. Automatic Construction: see how my programs build (random) prime magic squares of order 12, 15, 17 and 22. Double Square: I build a double square of order 12. See how. Order 35: My program now generate a 35 order prime magic square. Order 124: Yes this high order was generate in semi-automatic mode in a time that I think below of order 35. The order 191 seems near my hand... Muncey Construction: I have suppose the steps used by Muncey to build his 12 order square. Other primes: Here the true prime sequence...

54. Magic Square A report about Magic Squares 8 . 1 . 6 .. 3 . 5 . 7 .. 4 . 9 . 2 .. http://www.mathematische-basteleien.de/magsquare.htm

Magic Square Contents of this Page What is a Magic 3x3 Square? The Magic 3x3 Square The Magic 4x4 Square The Magic 5x5 Square The Magic nxn Square ... To the Main Page "Mathematische Basteleien" What is a Magic 3x3 Square? You can assemble the numbers 1 to 9 in a square, so that the sum of the rows, the columns, and the diagonals is 15. If you take the numbers 1 to 9, you have the standard square. 8+c 1+c 6+c 3+c 5+c 7+c 4+c 9+c 2+c A magic square remains magic, if you change each numbers by a constant c. You add c on the left. You can also subtract, multiply or divide. You define 4x4-, 5x5-... squares correspondingly. The Magic 3x3 Square top You have 1+2+3+4+5+6+7+8+9=45. In a magic square you have to add 3 numbers again and again. Therefore the average sum of three numbers is 45:3=15. The number is called the magic number of the 3x3 square. You can also achieve 15, if you add the middle number 5 three times. You can reduce 15 in a sum of three summands eight times: The odd numbers 1,3,7, and 9 occur twice in the reductions, the even numbers 2,4,6,8 three times and the number 5 four times. Therefore you have to place number 5 in the middle of the magic 3x3 square. The remaining odd numbers have to be in the middles of a side and the even numbers at the corners.

55. Magic Square: Meaning And Definitions — Infoplease.com magic square Definition and Pronunciation Find definitions for http://dictionary.infoplease.com/magic-square

Site Map FAQ in All Infoplease Almanacs Biographies Dictionary Encyclopedia Spelling Checker Daily Almanac for Oct 31, 2010 Skip Navigation Home Halloween ... games, quizzes Editor's Favorites Halloween Infoplease's Facebook page Follow Infoplease on Twitter Conversion Calculator ... DK Daily Teach Search: Infoplease Info search tips Search: Biographies Bio search tips Share Dictionary Find definitions for: a square containing integers arranged in an equal number of rows and columns so that the sum of the integers in any row, column, or diagonal is the same. Random House Unabridged Dictionary, magic realism Magindanao Cite Print ... Add to Reddit See also: magic square (Thesaurus) magic square (Encyclopedia) Related Content Daily Word Quiz: ailurophobia Analogy of the Day: Spelling Bee: reticent Crossword: Crossword Puzzle Guide Frequently Misspelled Words Frequently Mispronounced Words Easily Confused Words Find definitions for: Click Here! Click Here! Calculator Spelling Checker Place Finder Distance Calculator ... Year by Year 24 X 7 Private Tutor 24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring Explore Precalculus Mathematics RSS About Infoplease Part of Family Education Network Contact Link to Us Advertise with Infoplease Privacy ... Online Gradebook Click Here!

56. Magic Square A (normal) magic square consists of the distinct positive integers 1, 2, , such that the sum of the numbers in any horizontal, vertical, or main diagonal line is http://sjalam.tripod.com/MagicSquare.htm

Build your own FREE website at Tripod.com Share: Facebook Twitter Digg reddit document.write(lycos_ad['leaderboard']); document.write(lycos_ad['leaderboard2']); PUZZLE-01 (MORE SQUARES) PUZZLE-02 SQUARES-1 ... PRIME NUMBERS Magic Square A (normal) magic square consists of the distinct positive integers such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same magic constant The unique normal square of order three was known to the ancient Chinese, who called it the Lo Shu . A version of the order 4 magic square with the numbers 15 and 14 in adjacent middle columns in the bottom row is called D�rer's magic square . Magic squares of order 3 through 8 are shown above. The magic constant for an th order magic square starting with an integer and with entries in an increasing arithmetic series with difference between terms is (Hunter and Madachy 1975). If every number in a magic square is subtracted from

57. 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

58. Magic Squares An normal magic square is an arrangement of the numbers 1, 2, 3, n 2 in a square array, with the property that the sum of every row and column, as well as both diagonals, is the http://www.jcu.edu/math/Vignettes/magicsquares.htm

Vignette 20 Magic Squares An normal magic square is an arrangement of the numbers 1, 2, 3, ... n 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 of a normal magic square is You can verify that each of the three rows, the three columns, and the two diagonals add to 15. Magic Squares in History Magic squares have been studied for at least three thousand years, the earliest recorded appearance dating to about 2200 BC, in China. In the 9 th magic square with some very interesting properties is attributed to him. What is the Magic Sum? Given an normal magic square, suppose M is the number that each row, column and diagonal must add up to. Then since there are n rows the sum of all the numbers in the magic square must be . But the numbers being added are 1, 2, 3, ... n , and so 1 + 2 + 3 + ... + n . In summation notation, . Using the formula for this sum, we have , and then solving for M gives . Thus, a normal magic square must have its rows, columns and diagonals adding to

59. The Magic Square Although our website isn't up and running yet our new cd is available from our good friends at Ossian USA and from CDBaby. The lineup on the new recording consists of Dave Cory http://themagicsquare.com/

Although our website isn't up and running yet our new cd is available from our good friends at Ossian USA and from CDBaby . The lineup on the new recording consists of Dave Cory; banjo, bodhran and guitar, Ted Davis; guitar and flute, Eliot Grasso; uilleann pipes and flute, Aaron Olwell; fiddle flute and concertina and your humble narrator (Dan Isaacson); flute and whistle. Johnny B. Connolly was also kind enough to join us for a couple of guest spots on accordion and melodeon. Any questions or comments will please be directed to myself ( dandandan@themagicsquare.com Please stay tuned for the new site and thank you for your attention to our imaginary band. MEDIA ALERT: listen to an interview with Dan with Baltimore's WYPR.

60. Magic Square - Wolfram Demonstrations Project A magic square is a square array of the numbers 1, 2, , arranged so that the sum of the numbers in a row, column, or main diagonal is constant. http://demonstrations.wolfram.com/MagicSquare/

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