
	Where results make sense

Topic: Panmagic square

Related Topics

Magic constant

Prime reciprocal magic square

Antimagic square

Magic star

Bimagic square

Trimagic square

Magic cube

Multimagic square

Magic tesseract

Diabolic square

Heterosquare

LUX method for magic squares

Eight queens puzzle

	Magic square - Wikipedia, the free encyclopedia
		In mathematics, a magic square of order n is an arrangement of n Â² numbers in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.
		The earliest magic square of order four was found inscribed Khajuraho, India, dating from the eleventh or twelfth century; it is also a so-called diabolic or panmagic (pandiagonal magic square) where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.
		In the magic square of order four, the numbers in the four central squares and one square at each corner are retained in the same place and the others are interchanged with their diametrically opposite numbers.
	en.wikipedia.org /wiki/Magic_square (1547 words)

	Square (Site not responding. Last check: 2007-11-05)
		Mandarin square A mandarin square is a large embroidered badge sewn onto the surcoat of an official during the China.
		Square of opposition The Square of Opposition is a term from the study of Term Logic in which the logical relationship b...
		Squaring the square A square with sides equal to a unit length multiplied by an integer is called an integral square.
	www.brainyencyclopedia.com /topics/square.html (3008 words)

	Encyclopedia: Magic square
		A panmagic square is a magic square with the additional requirement that all broken diagonals sum to the magic constant.
		An antimagic square of order n is an arrangement of the numbers 1 to n² in a square, such that the n rows, the n columns and the two diagonals form a sequence of 2n + 2 consecutive integers.
		In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the sum of the numbers on each row, each column, each pillar and the four main space diagonals is...
	www.nationmaster.com /encyclopedia/Magic-square (3187 words)

	Collection of strange Magic Squares
		Saturn Magic Square : the magic costant is 15 and the sum of all the numbers of the square is 45.
		The sum of all the numbers of the square is 666, the number of the Beast of th Apocalypse.
		Mercury Magic Square : the magic costant is 260, the sum of all the numbers of the square is 2080.
	www.geocities.com /CapeCanaveral/Lab/3469/examples.html (593 words)

	Magic square (Site not responding. Last check: 2007-11-05)
		In mathematics, magic squares consist of a number of integers arranged in the form of a square in such a way that the sum of the numbers in every row, column and diagonal are the same.
		Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist, including the LUX method for magic squares, originally due to John Conway.
		Certain other restrictions can be imposed on magical squares, resulting, for example, in bimagic, trimagic and multimagic squares, and there are also other forms displaying similar characteristics, including magic circles, magic polygons, and magic cubes.
	www.sciencedaily.com /encyclopedia/magic_square (1338 words)

	[No title]
		The compound order panmagic square is the most illusive, it is proven that doubly odd order panmagic square don't even exist.
		An investigation of an order 15 panmagic square showed me that it is even possible to have non-panmagic components within a panmagic square, below I present preliminairy generalisations of things found, future investigation might change the position taken below.
		square, off sums in one component can be compensated by off sums in an other component.
	home.wanadoo.nl /aaledewinkel/Encyclopedia/p/Pan_CompoundOrder.html (668 words)

	puzzel25-2 magic squares
		For example, the square array opposite is a magic square of order 3 (the order is the number of horizontal rows or vertical columns), the constant sum of which is 15.
		The magic square of order 3 shown above is not panmagic, but the magic square of order 4 can be panmagic because the numbers in each of the four rows, four columns, and eight diagonals all could add up to an equal total.
		A magic square is called bimagic or doubly magic if it remains a magic square when each element is replaced by its square; it is called trimagic or triply magic if it remains a magic square when each element is replaced by its square and its cube.
	www.creativepuzzels.nl /spel/speel1/puzzel25-2.htm (455 words)

	Most-perfect magic square - Wikipedia, the free encyclopedia
		A most-perfect magic square of order n is a magic square containing the numbers 0 to n Â² â’ 1 with two additional properties:
		Apart from the trivial case of the first order square, most-perfect magic squares are all of order 4 n.
		They also show that there is a one-to-one correspondence between reversible magic squares and most-perfect magic squares.
	en.wikipedia.org /wiki/en:most-perfect_magic_square (157 words)

	Magic Square
		Squares which are magic under multiplication instead of addition can be constructed and are known as
		The 880 squares of order four were enumerated by Frenicle de Bessy in the seventeenth century, and are illustrated in Berlekamp et al.
		Attractive patterns are obtained by connecting consecutive numbers in each of the squares (with the exception of the Sun magic square).
	sjalam.tripod.com /mag-square3.htm (957 words)

	Magic Square
		Unlike the 3x3 square there is not just one conclusion for the distribution of the numbers 1 to 16 in a 4x4 square.
		The Latin square, which is formed by 1,2, and 3 and has different numbers in every row and column, is an example of a semi-magic square.
		A square is panmagic, if it is magic and if the numbers have the same sum in the corners, in the centre and on the edges.
	www.mathematische-basteleien.de /magsquare.htm (920 words)

	The 9 x 9 Pan-Magic Squares
		In addition, amongst odd-order panmagic squares, most interest was focused on the regular prime number squares.
		As with smaller squares, it is advantageous to fix the zero position by assigning the value zero to the letter "A" in all four character positions.
		When the composite alphabetical square is substituted with the numerical values in the table we get this order-9, pan-magic square with a magic sum of 360.
	www.grogono.com /magic/9x9.php (1135 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Latin Square Components form the basic squares with digits in the radix of the orders prime factors, below (intend to be) a full listing of LSC's for order 9 obtained by the pattern augmentation sheme.
		The numbers listed with each 3 by 3 square is a full representation of that square by taking each cell as a ternairy digit, thus the square form a 9 digit ternairy number which correspond with the listed decimal number.
		Given the given identification it is thus possible to parametrize a panmagic square with 8 numbers (ie four (pattern,augmentator) pairs).
	home.wanadoo.nl /aaledewinkel/Encyclopedia/DataBase/Augmentation_LSC_09.html (10645 words)

	R: Various tests for the magicness of a square (Site not responding. Last check: 2007-11-05)
		A {em semimagic square} is one all of whose row sums equal all its columnwise sums (ie the magic constant).
		A {em magic square} is a semimagic square with the sum of both unbroken diagonals equal to the magic constant.
		A {em panmagic square} is a magic square all of whose broken diagonals sum to the magic constant.
	www.matematik.lu.se /help/R/.R/library/magic/html/is.magic.html (300 words)

	R: Various tests for the magicity of a square (Site not responding. Last check: 2007-11-05)
		A semimagic square is one whose row sums all equal its columnwise sums (ie the magic constant).
		A magic square is a semimagic square with the sum of both unbroken diagonals equal to the magic constant.
		A panmagic square is a magic square all of whose broken diagonals have sum to the magic constant.
	biom1.univ-lyon1.fr /library/magic/html/is.magic.html (182 words)

	Magic Squares
		A magic square, of ANY size with an ODD number of squares on a side, can be constructed using this method.
		"Panmagic" If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square (Kraitchik 1942, pp.
		Albrecht Dürer's famous engraving of" Melancholia" made in 1514 includes a picture of a 4 X 4 magic square.Interestingly, this square can be created using a simple "mod 4" method, but Dürer switched the 2 center columns so that it would read 1514, the date of his engraving.
	www.smith.mn /square.html (595 words)

	Iso-like Magic Stars
		Order-5 is the only order magic square that can form a fully isomorphic magic star because there are 25 numbers in the order-5 magic square and 25 numbers in a complete order-5 isolike magic star.
		This is caused because the corner numbers in the square must appear in 4 different lines; the row, the column, the diagonal and a pan-diagonal.
		The center row and center column of the quadrant magic square is common to 2 adjacent quadrants.
	www.geocities.com /CapeCanaveral/Launchpad/4057/panmagic.htm (2260 words)

	backtracking: 5 x 5 magic squares
		A mouseclick on any number of the green-bordered square ("number-pool") moves this number into the first empty field of the red-bordered square ("magic area"); a click on any number of the magic area brings the number back to its original place in the pool.
		A magic square of order 5 is to be constructed, depending on choice a panmagic and/or a symmetric or a bordered one.
		When a solution is found, the algorithm will stop, and in that case, a search for a next solution may be continued with the corresponding button.
	www.faust.fr.bw.schule.de /mhb/backtrack/mag5en.htm (150 words)

	Grogono Magic Squares Home Page
		A Magic square is intriguing; its complexity challenges the mind.
		This is particularly true when the Magic Carpet approach is used to analyze or construct a magic square, e.g., to construct an order four magic square, four magic carpets would be required using: 8 and 0; 4 and 0; 2 and 0; and 1 and 0.
		My fascination with magic squares grew from experimental attempts to count the total number of possible squares when squares which, apparently different, were really identical when appropriately reflected or rotated.
	www.grogono.com /magic (821 words)

	Linux Attack - Magic Square Generator (Site not responding. Last check: 2007-11-05)
		A "magic square" is a square grid of numbers where the totals of the numbers along each row, each column, and the two main diagonals of the square, are all equal.
		A "panmagic square" is a magic square where the totals along all the diagonals starting at one side and continuing until they reach the other, wrapping from the top to the bottom of the square, or vice-versa, are also equal to the magic constant.
		A square at an angle of 45° to the main square is drawn so that its corners touch the sides of the main square.
	www.metawire.org /~chrise/magicsquare.php?theme=-grey (745 words)

	Econ World - Magic Square -- From MathWorld - La economía global (Site not responding. Last check: 2007-11-05)
		Definition, examples, and construction of magic squares, including algorithms for odd, doubly and singly even squares.
		The Siamese method for generating magic squares produces panmagic squares for orders with...
		A semimagic square is a square that fails to be a magic square only because one or both of...
	www.econworld.com.ar /buscar.php?q=Magic+Square+--+from+MathWorld (158 words)

	Math::MagicSquare::Generator - Magic Square Generator
		A magic square is a square in which all numbers are different and the sums of all rows, all columns and the two diagonals are equal.
		(Well, the sum in a 1x1 square can be 0, if the single number is 0.) You can use this method to check if the square has been tampered with.
		will always return 2 for squares generated using this module (or 3 if it's a 1x1 square).
	cpan.uwinnipeg.ca /htdocs/Math-MagicSquare-Generator/Math/MagicSquare/Generator.html (282 words)

	[No title]
		The list below contains all possible panmagic squares order 5, and is a reordering of the list by M.
		Listed squares are representations in normalized positions of 25 squares each by pan-relocation thus a total of 3600 squares, with reflection and transposition an other factor of 2
		In case of a panmagic square one should thus find the square in the above listing and can associate a index number with it (either Encyclopedia's or Suzuki's)
	home.wanadoo.nl /aaledewinkel/Encyclopedia/DataBase/Normalized_Pan_Order05.html (138 words)

	Magic Squares
		Meanwhile, we might note that in the 5x5, 7x7, and 9x9 magic squares, not only are the diagonal totals the same as the rows and columns, but the two diagonals at equal distances from the center diagonal add to the same total when divided by two.
		An alphamagic is “A magic square for which the number of letters in the word for each number generates another magic square.
		Saturn Magic Square : the magic constant is 15 and the sum of all the numbers of the square is 45.
	www.halexandria.org /dward090.htm (2905 words)

	magic squares of order 4
		A magic square of size 4 x 4 is to be constructed, depending on choice a general, a panmagic or a symmetric one.
		If the Stop-option is activated, the algorithm will stop, whenever a solution is found, and in that case, a search for a next solution may be continued with the corresponding button.
		The blue bordered square always displays the last found solution.
	www.faust.fr.bw.schule.de /mhb/backtrack/mag4en.htm (157 words)

	search.cpan.org: Math::MagicSquare::Generator - Magic Square Generator
		3 16 9 22 15 This square is the output of 20 8 21 14 2 print Math::MagicSquare::Generator->new->as_string; 7 25 13 1 19 24 12 5 18 6 11 4 17 10 23 The sums of the rows are 65.
		A checker - returns the common sum if the square is magic, or undef if it's not.
		DWYM - return the square as a formatted string, piece of html or in CSV format.
	search.cpan.org /~juerd/Math-MagicSquare-Generator/Generator.pm (320 words)

	Magic Square (Math : Recreations) - Site Directory (Site not responding. Last check: 2007-11-05)
		Demonstration of the properties of a pan-magic square.
		Squares that remain magic after entries are raised to various powers.
		Publication focuses on historical and cultural attitudes towards the significance of the squares.
	www.site-directory.org /Top/Science/Math/Recreations/Magic_Square (776 words)

	The math behind the Siamese method of generating magic squares
		And since the whole square is on average filled with the average value and all pairs (except the center) sum to twice the average value, every associative semi-magic square must have the average value in the center, so the two conditions are equivalent for siamese squares.
		These two squares of course correspond to the i and j squares since the values in a Siamese square are i+n*j.
		Such a square with multiple values none of which repeat on any row or column are often called "latin squares", especially when they are written with letters instead of numbers.
	www.xs4all.nl /~thospel/siamese.html (6650 words)

	Science: Math: Recreations: Magic_Square (Site not responding. Last check: 2007-11-05)
		The Magic Square Record Includes short description of a magic square, rules for trying to break a magic square record and all the records between 1975 and now.
		Multimagic Squares Magic squares which remain magic after their entries are raised to various powers.
		MathWorld: Panmagic Square Demonstration of the properties of a pan-magic square.
	www.doska.info /Science/Math/Recreations/Magic_Square (836 words)

	How Many Diagonals In Hexagon - Surch
		Recognising of basic common polygons such as square, rectangle, star, triangle, pentagon, hexagon and octagon.
		the square and the hexagon with six equal sides, and...
		and along the two diagonals of the square leave the...
	www.surch.co.uk /how+many+diagonals+in+hexagon (387 words)

	6x6 Magic Square (Site not responding. Last check: 2007-11-05)
		This is the way to introduce at Magic Square.
		{A}, {B} and {C} are odd because square is panmagic square.
		But if square is magic sqaure, {X}+{y} must be odd.
	www.guru.gr.jp /~issei/msq/msq6.html (165 words)

	Open Directory - Science: Math: Recreations: Magic Square (Site not responding. Last check: 2007-11-05)
		MathWorld: Panmagic Square - Demonstration of the properties of a pan-magic square.
		Multimagic Squares - Squares that remain magic after entries are raised to various powers.
		Queens on magic squares - Try to put 8 queens on an 8x8 square such that the queens sit on prime numbers.
	dmoz.org /Science/Math/Recreations/Magic_Square (912 words)

Try your search on: Qwika (all wikis)