81. Rotas Opera Tenet Arepo Sator Magic Square Kelly. Some of the Enochian ``texts'' were also arranged in squares,of much larger size than the RotasSator magic square. David http://www.plexoft.com/DTF/Sator.html

An example of a ROTAS-SATOR square can be seen at the Mediterranean Gallery of the Manchester Museum . Following is a a quick and dirty collation of Classics-list comments on the ROTAS-SATOR square R O T A S O P E R A T E N E T A R E P O S A T O R Some references mentioned repeatedly: Walter O. Moeller: The Mithraic Origin and Meanings of the ROTAS-SATOR Square (Leiden: Brill, 1973). John Ferguson: The Religions of the Roman Empire (Cornell U.P., 1970), p.168. Edith Kovach in ``The Clearing House Column'' of Classical Outlook , issue of December/January 85-86. The discussion will be found at gopher://140.142.56.13/00/public/classics/classics.log9209 gopher://140.142.56.13/1m/public/classics/classics.log9412 gopher://140.142.56.13/1m/public/classics/classics.log9601a gopher://140.142.56.13/0R55951-61434-/public/classics/classics.log9601b ... gopher://140.142.56.13/1m/public/classics/classics.log9806d ZPE =

82. Square magic squares Definitions, Formulas, Background, and Constructions MagicSquare (Click for full page view). Definitions The elementary http://www.simplyweb.net/~houlton/square.html

Magic Squares Definitions, Formulas, Background, and Constructions (Click for full page view). Definitions The elementary magic figure is the magic square , a two-dimensional array of numbers in which the sum of every row, column, and diagonal is identical. This identical sum is called the magic number . The numbers of n-dimensional magic figures flow consecutively from 1 to m n , where m is the order (the number of elements along an edge of the figure), and n is the spacial dimension. Shown above is a 3x3 magic square; m = 3 and n = 2. Formulas m = order; number of elements along an edge of the figure n = spacial dimension 1. The sum for the magic number = [m(1 + m n 2. Number of rows and columns = nm n-1 3. The middle number = (1+m n 4. Number of diagonals = 2 n-1 Background "The construction of magic squares is an amusement of great antiquity; we hear of magic squares in India and China before the Christian era, while they appear to have been introduced to Europe by Moscopulus who flourished Constantinople early in the fifteenth century. "However, what was at first merely a practice of magicians and talisman makers has now for a long time become a serious study for mathematicians. Not that they have imagined that they would lead them to anything of solid advantage, but because the theory was seen to be fraught with difficulty, and it was considered possible that some new properties of numbers might be discovered which mathematicians could turn to account. This has in fact proved to be the case, for from a certain point of view the subject has been found to be algebraical rather than arithmetical and to be intimately connected with great departments of science such as the 'infinitesimal calculus,' the 'calculus of operations', and the theory of groups.

83. Durer's Magic Square Return to magic squares http://www.simplyweb.net/~houlton/durersquare.html

Return to Magic Squares Return to Magic Squares

84. Magic Square Of Squares. Herman Baer's magic square of Squares page. By Uri Raz.Report concerning magic square of squares (3x3) Jan/99 http://www.private.org.il/magic_square.html

Herman Baer's Magic Square of Squares page. By Uri Raz Report concerning magic square of squares (3x3) Jan/99 =============================================== In "Scientific American" VIII.98 Martin Gardner in his quarter century review mentioned the above problem : rows and columns to have the same magic some of distinct squares as well as both the diagonals. Of the latter I wasnt sure in the beginning, but at any rateI prefered to content my self with the so-relaxed version of the problem. On the other hand both solutions to the relaxed problem I succeeded to find have a square at least e , and we can put down an arrangement of equations like this : (1a') 71^2 - 66^2 = 5 * 137 = 685 = 5*137 [2] = (26, 3) = (19,18) 71^2 - 54^2 = 17 * 125 = 2125 = [4] = (46, 3) = (42,19) 71^2 - 51^2 = 20 * 122 = 2440 = 2^3*5*6 [2] = (46,18) = (42,26) 71^2 - 46^2 = 20 * 117 = 2925 = 3^2*5^2*13 [2] = (54, 3) = (51,18) 71^2 - 42^2 = 29 * 113 = 3277 = 29*113 [2] = (54,19) = (51,26) 71^2 - 26^2 = 45 * 97 = 4365 = 3^2*5*97 [2] = (66, 3) = (51,42) 71^2 - 19^2 = 52 * 90 = 4680 = 2^3*3^2*5*13 [2] = (66,18) = (54,12) 71^2 - 18^2 = 53 * 89 = 4717 = 53*89 [2] = (66,19) = (51,46) 71^2 - 3^2 = 68 * 74 = 5032 = 2^3*17*37 [2] = (66,26) = (54,46) (2'a) 79^2 - 74^2 = 5 * 153 = 765 = 3^2*5*17 [2] = (27, 6) = (21,18) 79^2 - 69^2 = 10 * 148 = 1480 = 2^3*5*37 [2] = (38, 6) = (34,18) 79^2 - 66^2 = 13 * 145 = 1885 =

85. StudyWorks! Online : Tasty Magic Square Solution Who Said What? StudyWorks Challenge. Challenging Puzzles. Tasty magic squareSolution. Here is the solution. Tasty magic squares December 26, 2001. http://www.studyworksonline.com/cda/content/article/0,,NAV3-39_SAR1565,00.shtml

Games Puzzle of the Week Archives of Previous Puzzles Alien Sphere ... Challenging Puzzles Tasty Magic Square Solution Here is the solution. Tasty Magic Squares: December 26, 2001

86. Magic Square-magic Tricks magic square, Tell A Friend 0. PRESENTATION Lay out the nine cards ina 3 by 3 gridor magic square-in numerical order as illustrated. http://www.triviaplanet.com/baffle your friends/magic_square.html

MAGIC SQUARE Tell A Friend Even though you have a free choice of where you will move in a magic square of nine playing cards, I know exactly where you will end up. And when you show your family and friends so will you! . REQUIREMENTS: YOU WILL NEED NINE PLAYNG CARDS- THE ACE,THREE,FIVE,SEVEN AND NINE OF HEARTS AND THE TWO,FOUR,SIX AND EIGHT OF SPADES. PREPARATION: Remove 9 red cards and 9 black cards from the deck. Write "THERE WILL BE 2 MORE BLACK CARDS IN THE LONG ROW THAN RED CARDS IN THE SHORT ROW !" on a peice of paper and then seal it inside an envelope. PRESENTATION: Lay out the nine cards in a 3 by 3 grid-or magic square-in numerical order as illustrated. Follow the instructions below. When I ask you to move,you can move to the card above or below or to the left or right of the card you are touching- but not diagonally. Choose any one of the red cards as your starting point. The choice is yours.

87. The Joy Of Smoking: Magic Square The Joy of Smoking. « OS X.2 Main Mr. Fun » January 24, 2003.magic square. This is neat SATOR AREPO TENET OPERA ROTAS. It means http://www.e-popp.com/arlen/blog/archives/000436.html

The Joy of Smoking Main January 24, 2003 Magic square This is neat: S A T O R A R E P O T E N E T O P E R A R O T A S It means something like "The sower Arepo holds the works of the wheels," the wheels referring to the nine celestial spheres of Ptolmaic cosmology. Arepo must be some code name for the big man upstairs or for a constellation. If anybody knows for sure, post a message. Posted by Arlen at January 24, 2003 04:18 PM Comments Post a comment Name: Email Address: URL: Comments: Remember info?

88. Make Your Own 5x5 Magic Square Explanation The numbers in the Red Squares form the 5x5 magic square. Thenumbers diagonals . You can make your own magic square in two ways. Try http://www.grogono.com/Magic/text-makeyourown5.shtml

Frames NO Frames Topic Index: Magic Carpets Make Your Own How Many? Spreadsheets ... Downloads Individual Magic Squares by Order: Regular Prime Pan-Magic Squares: Multiple Carpet Pan-Magic Squares: Magic Squares Home Page Grogono Home Page 4P+2 Magic Squares (6, 10 etc.): Make Your Own 5x5 Magic Squares Home Make Your Own: 3 x 3 4 x 4 5 x 5 The magic square below is the sum of the patterns that these numbers make. Use them or enter new ones and then click To understand the structure, move the mouse over the blue arrows and wait. Look at the pattern of your numbers in the square below The Bottom Right number (under the blue down arrow) above is the first number in the sequence for the square. By convention it is "1", but any number can be used. Try changing the bottom row above: use "5,4,3,2,1,0" instead, do you get the same result as "4,3,2,1,0,1"? You can also try experimenting by writing in your own numbers in the red squares. To see the totals, press The numbers at the top and the left are the sums for the diagonal rows - including the broken diagonals.

89. Durer's Square - A Magic Square - Art - Mason West durer's square a magic square. leda atomica salvador dali. , durer's square.a magic square. Back After a 32Year Hiatus, the British Museum's Dürer. http://mason-west.com/Art/durersquare.shtml

Bergman Art Photography Film Unforgiven Romance Body Humano Journal WRITINGS AUTHORS REVERBERATIONS art various artists a. c. radebaugh exhibit, opening february 2003, philadelphia edvard munch edvard munch choose munch by the death bed death in the si... dead mother and... the scream anxiety evening on karl... self-portrait w... pablo picasso pablo picasso 20th-century artistic genius Choose Picasso science and cha... la vie, 1903 the tragedy, 1903 the family of s... les demoiselles... igor stravinsky... woman and child... women running o... portrait of dor... weeping woman, ... guernica, 1937 the mystery of ... the picasso sta... vincent van gogh a visual history of a tormented mind the self-portraits of Vincent Van Gogh diego rivera portrait diego rivera montparnasse diego rivera david siqueiros david siqueiros select siqueiros mural tropical ... self-portrait cauhtemoc revived self-protrait monument of cua... david siqueiros echo of a scream david siqueiros the devil in th... david siqueiros david siqueiros david siqueiros david siqueiros david siqueiros accident in the...

90. Magic Square Students opened a file with the following spreadsheet. They learnedhow to enter a formula in a spreadsheet so that the totals would http://www.joannegoodwin.com/technology/5th/magic/

Students opened a file with the following spreadsheet. They learned how to enter a formula in a spreadsheet so that the totals would be calculated as they entered the digits. To enter the formula for finding the sum: Click in the cell where you want sum. For example: click to highlight cell A4. In the text entry bar, type an equal sign. All formulas begin with this symbol. Then click in the cells you want to total. For our example: click in cells A1, A2, and A3. Notice the formula in the text entry bar. When you press return you will enter the formula and the computer will make your calculations. Until digits are entered in the cells your total will be zero. Follow this procedure for each row and column. Back to the CRS Tech Lab

91. Merlin's Magic Square Merlin's magic square. The applet consists of two 3x3 arrays. On theleft, the small one shows the target configuration. To modify http://www.cut-the-knot.com/Curriculum/Algebra/Merlin.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Merlin's Magic Square The applet consists of two 3x3 arrays. On the left, the small one shows the target configuration. To modify the target configuration, click on the squares you want modified. On the right, a bigger one holds the puzzle itself and, if the Hint box is checked, the hint or, rather, the solution to the puzzle. The hint configuration is also modifiable and the current state of the puzzle changes accordingly. States are represented by a cyclic arrangement of digits - the residues modulo the number of states. I allow only 2, 3, and 4 state buttons for two reasons. For one, with more states the puzzle grew too difficult for me to solve. The second reason will become apparent from the puzzle's theory. The effect of pressing a button is best described by the following diagram where the button pressed is colored red and the affected buttons are blue. Other corner and side moves have an analogous effect. The applet allows for a second puzzle. Imagine the buttons wrapped on a torus. Then all buttons have exactly the same number of "across-the-edge" neighbors, 4. (In Computer Graphics terms, these are 4-neighbors.) In this modification, all 4-neighbors of a pressed button advance their states along with the button itself. Naturally, the first puzzle is rather Plane whereas the second is played on a Torus . For technical reasons the latter is only played with 3-state buttons. The theory Alexander Bogomolny G o o g

92. Magic Square! www.angelfire.com/on/topfen/squares.html magic square magic square. MagicSquare! Move the numbers on the grid so that they read 18 in order. http://www.angelfire.com/on/topfen/squares.html

www.angelfire.com/on/topfen/squares.html magic square magic square Magic Square! Move the numbers on the grid so that they read 1-8 in order. The is the 'empty' square. Click on any number next to and they will switch places. Good luck! # of moves: Homepage Learn English English Tests Learning Links ... Recipes

93. A Magic Square Solving Program In a 3x3 magic square each row column and the two diagonals add up to 15.Each cell holds one value from 1 to 9 without repeating any values. http://www1.minn.net/~dchristo/Magic3/Magic3.html

Here is an Applet which Helps find 3 x 3 Magic Squares. In a 3x3 Magic Square each row column and the two diagonals add up to 15. Each cell holds one value from 1 to 9 without repeating any values. Here is an example. Enter any three of these numbers, with not more than two in the same row or column. Press the Solve Button and it will find the other 6.

94. Re: Looking For Anagram Magic Square Subject Re Looking for anagram magic square. By SONIA ARCHER on August05, 19102 at 195113 In Reply to Re Looking for diagramless http://www.litsoft.com/CrossTalk/challenge/messages/133.html

Subject: Re: Looking for anagram magic square By SONIA ARCHER on August 05, 19102 at 19:51:13: In Reply to: Re: Looking for diagramless posted by Warren Rivers on April 04, 19101 at 06:02:18: Follow Ups Post Followup Forum I REALLY ENJOY THE ANAGRAM MAJIC SQUARE AND THE PLACES PLEAS PUZZLES ARE THERE ANY BOOKS ON THESE BY THEMSELVES? IF SO WHERE CAN I GET THEM? Follow Ups: Re: Looking for anagram magic square demetra Re: Looking for anagram magic square Warren Rivers Post a Followup Name: E-Mail: Subject: Comments: Follow Ups Post Followup Forum

95. Re: Looking For Anagram Magic Square Subject Re Looking for anagram magic square. In Reply to Re Looking for anagrammagic square posted by SONIA ARCHER on August 05, 19102 at 195113 http://www.litsoft.com/CrossTalk/challenge/messages/147.html

Subject: Re: Looking for anagram magic square By demetra on October 20, 19102 at 19:02:42: In Reply to: Re: Looking for anagram magic square posted by SONIA ARCHER on August 05, 19102 at 19:51:13: Follow Ups Post Followup Forum I LOVE THE ANAGRAM MAGIC SQUARES!!! WHERE CAN I GET MORE? THERE SHOULD BE A BOOK WITH ONLY ANAGRAM MAGIC SQUARES IN THEM. Follow Ups: Post a Followup Name: E-Mail: Subject: Comments: Follow Ups Post Followup Forum

96. ABRAXASIXAXIS MAGIC SQUARE The B AbraxasIxAxis magic square /B was channelled by Orryelle Defenestrate/Basculeafter a fly agaric journey. It was activated http://www.crossroads.wild.net.au/msq.htm

THE ABRAXASIXAXIS MAGIC SQUARE: I I I I I I A I I I I I I I S I S/ I/ A B R A X A S/ I I/ I S I S/ I R I S/ I S/ A S I S/ I X I X/ A S/ I S I S/ I I/ A X I S/ I X/ I S/ I S I S I/ A/ I X I X/ A S/ I S I S/ I A B R A X A S/ ... S I R I S/ I S/ I X I X/ I S/ I I/ A S/ I S/ I X/ I S/ I S I S I X/ I S I S/ A S / I S I S/ I I/ A S/ I S/ I X/ A S/ I S I S I S/ A S/ I S I S/ I S/ I X/ I I/ I S I S/ I S/ I S I S/ I S I channelled the ABRAXASIXAXIS MAGIC SQUARE Imbolc full moon '97 . During the trip I read Austin Osman Spare 's 'Rechtaw' evocation. The only line of this evocation which I didn't fully understand was the last, where it shifted to invocation: 'By the sacred word-graph of heaven, I invoke thee...' There were no immediate obvious effects from the invocation, until many hours later while cooking a hen's egg in the mushroom-brewing pot at dawn I began channelling information about the gnostic deity Abraxas being the axis of Abr' , which seemed to represent both Abrahadabra (word of magical manifestation) and Abramelin the mage, an ancient magus whom I remembered had created or revealed several

97. Mathematics Mega-Magic Square The Megamagic square Did you enjoy the standard magic square? The onebelow answer. Click here to submit mega-magic square. or click http://www.sec.org.za/maths/mfun4x4.html

The Mega-Magic Square Did you enjoy the standard magic square? The one below is a real brainteaser but from your experience with 3rd order magic squares it should be possible to crack the 16 number jackpot. Whereas in a 3rd order magic square only one number configuration (the 5 always in the middle, at the corners 2, 4, 6 and 8 which can be rotated but not replaced by other numbers) will yield the desired result, a smart French mathematician F. de Bessy found out a long time ago that there are 880 possible number configurations for a 4x4 magic square! No wonder they are called 'mega-magic squares'. Better you apply a similar method as with the 3rd order square, a giga effort and just work it out. Good luck! In a big square containing sixteen small squares the numbers 1 to 16 are distributed in a way that the sum of all four rows, all four columns and the two diagonals adds up to the same number. a b c d e f g h i j k l m n o p row: a + b + c + d = x column: a + e + i + m = x diagonal: a + f + k + p = x Have you come up with one of the 880 solutions?

98. MAGIC SQUARE VOCABULARY magic square VOCABULARY (Lois Hoshijo). Descriptor I chose to use a 3 x3 magic square that was an example from Art Scholastic (1993). The http://linus.icoe.org/reading/cal/magicsquare.htm

MAGIC SQUARE VOCABULARY (Lois Hoshijo) Descriptor and Setting: Content Area Literacy "Magic Square" Math Vocabulary Strategy—Lois Hoshijo used the "Magic Square" vocabulary strategy in her middle school classroom to assess students' knowledge of definitions of mathematical terms. The procedure that Lois used is described by her as follows: I chose to use a 3 x 3 Magic Square that was an example from Art Scholastic (1993). The numerical total for each vertical, horizontal, and diagonal row was 18. I organized my activity with three separate sections: a) the 3 x 3 square each labeled with a letter, b) the list of content area terms, and c) the list of definitions for those mathematical terms. Students were directed to match each term with the appropriate definition, while they also considered the numbers denoting the terms as well as the letters denoting the definitions. Once the match was made, the number of the correct mathematical term was placed in the proper space of the square that was marked by the letter of the matching definition. Students were not informed about what the correct total of the Magic Square was. If their matches were correct, the Magic Square would be completed.

99. Frank Morgan's Math Chat - Fractional Magic Square September 6, 2001. Fractional magic square. Complete the following to a magic square,in which each column, each row, and both diagonals sum to 1. 3/8, _, _. http://www.maa.org/features/mathchat/mathchat_9_06_01.html

Frank Morgan's Math Chat September 6, 2001 Fractional Magic Square Math Chat wishes all students and teachers a happy and satisfying new academic year. Old Challenge: (National Public Radio Weekend Edition Puzzle 7/29/01). Complete the following to a magic square, in which each column, each row, and both diagonals sum to 1. Answer: Sudipta Das of Calcutta, India and R. Weirauch use the fact (proved by Weirauch and early the next morning by my house guest and college roommate Randy Kimble) that the center entry must be the average value of 1/3, as you might expect. (All columns, rows, and diagonals sum to 1.) It is now easy to fill in the rest. The middle left entry must be 5/12, then the bottom left entry must be 5/24, and so on. Here is Weirauch's proof that the center entry equals 1/3. Consider a square a b c d e f g h i Adding both diagonals plus the middle row yields 3 = (a + e + i) + (c + e + g) + (d + e + f) = 3e + (a + d + g) + (c + f + i) = 3e + 2. Therefore 3e = 1 and e = 1/3.

100. Explorer: Magic Square 12 & 15 magic square 12 15. Click here to receive a 6 KByte HQX file. Includes directionson how to solve a 3 x 3 magic square, as well as, a magic square 12. http://unite.ukans.edu/explorer/explorer-db/html/810757742-81ED7D4C.html

Click here to receive a 6 KByte "HQX" file. Click here to receive a 8 KByte "PDF" file. Resource Type Instructional Aid Physical Media Downloadable File Grades Availability ECNet Description Presents a problem solving activity incorporating the use of a grid to be filled with numbers in order that each row, column and diagonal adds up to 15. Includes directions on how to solve a 3 x 3 Magic square, as well as, a Magic Square 12. Curriculum Mathematics/Problem Solving and Reasoning/General Problem Solving and Reasoning Mathematics/Problem Solving and Reasoning/Understanding Problems Mathematics/Problem Solving and Reasoning/Problem Solving Strategies Mathematics/Problem Solving and Reasoning/Evaluating Solutions Mathematics/Problem Solving and Reasoning/Logical Reasoning Mathematics/Whole Numbers and Numeration/Addition ProcessSkills Mathematics Process/Computation Mathematics Process/Problem Solving Author Tobler, Karen Publisher Great Lakes Collaborative, 9555 Haggerty Rd., Belleville, MI 48111 Publication Date Cost In US Dollars Reviewers Karen Tobler Dolores Veshka Edit Resource Explorer Home Search Comments ... Help Generated by Unite Software on April 21, 1998 12:01 AM.

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