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Topic: Bimagic square

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Bimagic cube

Trimagic square

Trimagic cube

Antimagic square

Multimagic square

Magic cube

Magic constant

Panmagic square

Multimagic cube

Magic star

Diabolic square

Magic tesseract

Heterosquare

LUX method for magic squares

Prime reciprocal magic square

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	Magic square - Wikipedia, the free encyclopedia
		The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.
		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 (due to John Conway) and the Strachey method for magic squares.
		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 (1488 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 (585 words)

	Magic_square
		In mathematics, a magic square of order n is an arrangement of n² 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.
		The magic square figures in Greek writings dating from about 1300 BC and was used by Arabian astrologers in the ninth century when drawing up horoscopes.
	www.apawn.com /search.php?title=Magic_square (1584 words)

	Multimagic square - Wikipedia, the free encyclopedia
		In mathematics, a P-multimagic square is a magic square that remains magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ P.
		Thus, a magic square is bimagic if it is 2-multimagic, and trimagic if it is 3-multimagic.
		The first 4-magic square, of order 512, was constructed in May 2001 by André Viricel and Christian Boyer; about one month later, in June 2001, Viricel and Boyer presented the first 5-magic square, of order 1024.
	en.wikipedia.org /wiki/Multimagic_square (136 words)

	Encyclopedia: Bimagic square
		The first known bimagic square has order 8 and magic constant 260; it has been conjectured by Bensen and Jacoby that no nontrivial bimagic squares of order less than 8 exist.
		In mathematics, a P-multimagic square is a magic square that remains magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ P. Thus, a magic square is bimagic if it is 2-multimagic, and trimagic if it is 3-multimagic.
		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/Bimagic-square (553 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)

	[No title] (Site not responding. Last check: 2007-10-21)
		The first bimagic square in the world has been built by G. Pfeffermann in France in 1890.
		This 8x8 square was published in a french magazine "Les Tablettes du Chercheur" january 15, 1891, with only the half of the numbers.
		The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", february 1st 1891.
	home.wanadoo.nl /aaledewinkel/Encyclopedia/DataBase/PfeffermannSquares.html (688 words)

	magic square
		The Lo Shu Square, as the magic square on the turtle shell is called, is an important part of Feng Shui, the ancient Chinese art of geomancy.
		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 pandiagonal magic square where, in addition to the rows, columsn and main diagonals, the broken diagonals also have the same sum.
		Magic squares were frequently found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity, prevention against diseases etc..
	www.fact-library.com /magic_square.html (1194 words)

	MULTIMAGIE.COM - The smallest possible bimagic square
		The known smallest bimagic squares are 8th-ordered, which is the same order as the first bimagic discovered in 1890 by Pfeffermann.
		Because it is proved, as already seen, that a 7th-order bimagic square has to use a pair of bimagic series of 7 odd numbers among the 60 existing series, Walter Trump directly searched -as I did- squares using a pair of these series.
		It means that the impossibility of a 7th-order bimagic square is not coming from an impossibility to arrange its squared integers in magic square.
	cboyer.club.fr /multimagie/English/Smallestbi.htm (1757 words)

	Magic square (Site not responding. Last check: 2007-10-21)
		The number of basic magic squares of any higher degree is not yet known but it was estimated by Klaus Pinn and C. Wieczerkowski (1998) using Monte Carlo simulation and methods from statistical mechanics to be (1.7745 ± 0.0016) × 10
		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.
		When a move would leave the square, it is wrapped around to the first row or column, respectively.
	www.sciencedaily.com /encyclopedia/magic_square (1332 words)

	9-fold Higher Order Patterning of Tao Te Ching Insights
		Bimagic squares are a subset of the class of multimagic squares; it is believed that no bimagic squares of order less than 8 exists (Benson and Jacoby 1976).
		A magic cube is a three-dimensional version of the magic square in which the rows, columns, pillars (or "files"), and four space diagonals each sum to a single number known as the magic constant.
		A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube.
	laetusinpraesens.org /docs00s/taote4.php (3509 words)

	Normal bimagic square
		Following bimagic square is made by "Mahoujin" (Magic square) which is written by Kiyomi Oomori method.
		Example: Trimagic square is a magic square that is still magic when each cell of the square is squared or cubed.
		Order-3 magic square is only one, it cannot keep magic when each cell of the square.
	www.geocities.co.jp /HeartLand-Gaien/8690/houjin/en/double.html (707 words)

	Magic Squares: bimagic
		It is known today that there are no bimagic squares of orders less than 8.
		All bimagic squares of orders less than 8 are build with non-consecutive numbers.
		There are also bimagic squares of order 8 and 9 with additionally properties.
	www.magic-squares.de /properties/multimagic/orders.html (210 words)

	Puzzle 287. Multimagic prime squares
		A magic square is bimagic (or 2-multimagic) if it remains magic after each of its numbers have been squared.
		By extension, a square is P-multimagic if it remains magic after each of its numbers have been replaced by their k-th power (for k=1, 2,..., to P).
		A 3x3 bimagic square using distinct integers (or of course prime integers) is proved to be impossible.
	www.primepuzzles.net /puzzles/puzz_287.htm (651 words)

	Magic Square (Site not responding. Last check: 2007-10-21)
		Even numbers which were missed are then added sequentially along the continuation of the diagonal obtained by wrapping around the square until the wrapped diagonal reaches its initial point.
		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).
	www.math.sdu.edu.cn /mathency/math/m/m029.htm (1094 words)

	Amazon.com: Books: The Zen of Magic Squares, Circles, and Stars : An Exhibition of Surprising Structures across ... (Site not responding. Last check: 2007-10-21)
		A magic square is an array of numbers in which the sums of numbers in rows, columns, and diagonals are equal.
		A magic square is a square grid of numbers where the row and column sums are the same.
		Magic squares can be created using many different formulas, including the moves of a knight on a board, using operations other than addition, and the embedding of magic squares inside magic squares.
	www.amazon.com /exec/obidos/tg/detail/-/0691115974?v=glance (1829 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 (2887 words)

	Trimagic Square (Site not responding. Last check: 2007-10-21)
		Magic Square, the square is said to be a trimagic square.
		Trimagic squares of order 32, 64, 81, and 128 are known.
		Tarry gave a method for constructing a trimagic square of order 128, Cazalas a method for trimagic squares of orders 64 and 81, and R.
	mathserver.sdu.edu.cn /mathency/math/t/t365.htm (86 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Magic squares are square arrays of numbers, n units on a side, consisting only of the numbers {1,2,3 n2}.
		We see it comes out to a square looking like this: 17241815235714164613202210121921311182529 Muhammad was eventually able to construct many magic squares of higher orders with his new formulas (“Muhammad”).
		Muhammad recognized how the magic squares could be rotated around many different axes without changing their properties, creating new magic squares that were simply reflections of previous ones (Drum and Winstead).
	massasoit.ath.cx /out/Math/muhammad.doc (1161 words)

	ultramagic squares of order 7 - samples (Site not responding. Last check: 2007-10-21)
		Additionally the squares of these numbers have equal sums (bimagic feature).
		: The center row and the center column are 'trimagic', their numbers have equal sums, this is also true for squares of the numbers and for the third powers of the numbers.
		Each square is shown twice with different yellow magic squares (diamonds) of order 3.
	www.trump.de /magic-squares/ultramagic-7/samples.htm (167 words)

	Welcome to Mathsoc
		Hence, this 11 square* cannot be considered as a Magic square.
		As far as the Magic Squares of even Orders are concerned, the trends are certainly more interesting to follow.
		If replacing each number by its square in a Magic Square produces another Magic Square, the square is said to be a bimagic square.
	mathsoc.cms.gre.ac.uk /mathematicstriviamagicsquare.htm (647 words)

	Multimagic Cubes
		I have a similar page that illustrates multimagic squares.
		This Pfeffermann bimagic square [1] was converted into a magic cube by A. Huber [2].
		The sum is 130 in the 16 columns, 16 rows, 16 pillars, and in the 4 main diagonals of the cube.
	members.shaw.ca /hdhcubes/cube_multimagic.htm (2270 words)

	John R. Hendricks - Welcome
		Then, suddenly I would try something a bit different by using a bimagic square as a reference and a “finer-grained” coordinate system and the addition of a new z- direction.
		Sixty years of experience has taught me that it is sometime easier to make a large magic square than a small one and this could be true for cubes too.
		Now, if you square all the numbers in the cube and thereby obtain a new magic cube, the various required sums will be given by Equation (2) instead.
	members.shaw.ca /johnhendricksmath (622 words)

	Multimagic Squares
		However, a bimagic square has the additional property that if each number in the square is multiplied by itself (squared, or raised to the second power) the resulting row, column, and diagonal sums are also magic.
		In addition, a trimagic square has the additional property that if each number in the square is multiplied by itself twice (cubed, or raised to the third power) the square is still magic.
		Also presented is one of a family of order 9 bimagic squares with special properties (which also appear in the cube).
	www.geocities.com /~harveyh/multimagic.htm (762 words)

	Bimagic square - TheBestLinks.com - Mathematics, 1998, Magic square, Magic cube, ...
		Bimagic square - TheBestLinks.com - Mathematics, 1998, Magic square, Magic cube,...
		Bimagic square, Mathematics, 1998, Magic square, Magic cube, Bimagic cube...
		You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
	www.thebestlinks.com /Bimagic_square.html (150 words)

	Magic Squares (Site not responding. Last check: 2007-10-21)
		The famous Loh-Shu from 2800 B.C. It is the oldest known magic square of the world.
		And you have the possibility to create millions of other, different magic squares online on these pages.
		These pages use CascadingStyleSheets (CSS) and JavaScript and are optimized for MS Internet-Explorer and Netscape assuming a screen resolution of 800x600 or more.
	www.magic-squares.de /magic.html (56 words)

	Bimagic square . Bimagic cube . Multimagic square . Trimagic square (Site not responding. Last check: 2007-10-21)
		Magic cube Trimagic cube Multimagic cube Magic square Bimagic square Trimagic square Multimagic square...
		In mathematics, a P -multimagic square is a magic square that remains magic even if all its numbers...
		Magic square Bimagic square Multimagic square Magic cube Bimagic cube Trimagic cube Multimagic cube...
	www.uk.fraquisanto.net /Bimagic_square (412 words)

	Trimagic square - Encyclopedia Glossary Meaning Explanation Trimagic square (Site not responding. Last check: 2007-10-21)
		Trimagic square - Encyclopedia Glossary Meaning Explanation Trimagic square.
		Here you will find more informations about Trimagic square.
		The orginal Trimagic square article can be editet
	www.encyclopedia-glossary.com /en/Trimagic-square.html (135 words)

	Bimagic square -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Bimagic square -- Facts, Info, and Encyclopedia article
		However, (Click link for more info and facts about J. Hendricks) J.
		(A square matrix of n rows and columns; the first n-squared integers are arranged in the cells of the matrix is such a way that the sum of any row or column or diagonal is the same) Magic square
	www.absoluteastronomy.com /encyclopedia/b/bi/bimagic_square.htm (190 words)

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