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Topic: Magic constant

Related Topics

Magic tesseract

Magic star

Magic cube

Antimagic square

Panmagic square

Bimagic square

Multimagic square

Trimagic square

Diabolic square

Heterosquare

Prime reciprocal magic square

LUX method for magic squares

Eight queens puzzle

	Magic square - Wikipedia, the free encyclopedia
		In mathematics, a magic square (幻方) 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 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.
	en.wikipedia.org /wiki/Magic_square (1488 words)

	Magic number - Wikipedia, the free encyclopedia
		Magic number - in sports, a number used to indicate how close a front-running team is to clinching a season title;
		Magic number - in nuclear physics, a number of nucleons such that they are arranged into complete shells within the atomic nucleus.
		Magical number seven - in cognitive psychology, a short-term memory theory involving chunking.
	en.wikipedia.org /wiki/Magic_number (155 words)

	NCTM : Illuminations : Magic Squares: Discovering Their History and Their Magic
		Magic squares have a rich history dating to around 2200 B.C. A Chinese myth claimed that while the Chinese Emperor Yu was walking along the Yellow River, he noticed a tortoise with a unique diagram on its shell (see fig.
		Magic squares in China have been used in various areas of study, including astrology; divination; and the interpretation of philosophy, natural phenomena, and human behavior.
		If magic squares were, in general, small models of the Universe, now they could be viewed as symbolic representations of Life in a process of constant flux, constantly being renewed through contact with a divine source at the center of the cosmos.
	illuminations.nctm.org /print_lesson.aspx?id=263 (2047 words)

	Magic Water Savings (Site not responding. Last check: 2007-10-21)
		A flow limiter is a component which maintains a constant flow rate independent of line pressure.
		Magic flow regulators automatically provides a constant flow rate at any pressure between 1 bar and 10 bar.
		Magic Technologies flow regulators are built from a high precision o-ring and a very accurate housing.
	www.magic-tec.com (279 words)

	The SATOR Magic Square (Site not responding. Last check: 2007-10-21)
		A magic square is a square table (mathematicians call them "matrices") of numbers with the remarkable property that the sum of numbers on diagonals, rows and columns give the same number: of course one requires that the numbers appearing in the table are all different between them.
		This is a rather symmetric magic square since: the sum of numbers along sub-rectangles with six numbers is always 30 (this is obvious since the sum of rows and columns gives 15), and the sum of sub-triangles with four numbers is always 20 (also this is obvious).
		Magic squares were considered, also due to this mysterious origin, as talismans and amulets which can cure the health both of body and spirit.
	www.math.unifi.it /~caressa/math/sator.html (841 words)

	Games and Puzzles Journal #26
		In spite of the very large number of magic squares and knight's tours possible on doubly even boards, until now 16×16 was the smallest board size on which a ‘perfect magic tour’ (with both diagonals adding to the magic constant) were found.
		All the 266 magic knight tours found on the 8×8 board are ‘weak’ magic squares, since their diagonals do not add to the magic constant.
		Figures 26 and 27 are curious magic tours since the sums of their diagonals are equal but different from the magic constant.
	www.gpj.connectfree.co.uk /gpjh.htm (2135 words)

	Satanic square - Wikipedia, the free encyclopedia
		A satanic square is a magic square that remains magic after all its numbers are raised to a specific (fixed) power.
		This magic square has a magic constant of 260.
		It is another magic square with a magic sum of 11180.
	www.wikipedia.org /wiki/Satanic_square (89 words)

	[No title]
		Depending on the function used to combine numbers on a "magic line" several function types of magic hypercubes can be defined.
		Next to the addition magic hypercubes one thus can define subtraction, multiplication and division magic hypercubes, next to these of course this list can be expanded as suggested by the text below and the qualification article.
		Regularly the constant formula is observer on each 1-agonal and each n-agonal, leading to the magic constant
	home.wanadoo.nl /aaledewinkel/Encyclopedia/m/MagicHypercube.html (412 words)

	[No title]
		The main point of the project was to write a program that could generate magic squares of all sizes, but my research failed to uncover a workable algorith for Single Even sizes.
		Definition of a magic square: Although there are other types of squares called "magic", this program deals with the standard definition as follows.
		Magic squares are arrays of numbers where the rows, columns and the diagonals add up to the same number, (called the square's constant).
	www.wctatel.net /web/blevad/magic.rex (422 words)

	Magic Squares and Dihedral Group D4 (Site not responding. Last check: 2007-10-21)
		In the applet below, magic squares of order (size) 3, 5, 7 and 9 may be explored.
		To construct a magic square, the "diagonal" method is used which is based on a method introduced in Europe in 1693 by De la Loubere, who learned it while he was envoy to Siam.
		Magic squares are mentioned in Chinese mythology, which claims the oldest magic square, Lo Shu, appeared on a turtle's back in the river Lo in 2200 B.C..
	www.wou.edu /~burtonl/magic.html (414 words)

	Magic constant
		The magic constant of a magic square is the sum of numbers in any row, column, and diagonal of the magic square.
		For example, the magic square shown below has a magic constant of 15.
		The term magic constant is similarly applied to other "magic" figures such as magic stars and magic cubes.
	www.arikah.net /encyclopedia/Magic_constant (210 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}.
		What’s special about magic numbers, however, is that the numbers in any row, column, or main diagonal add up to the same number, called the magic constant.
		To find the magic constant for any magic square of order n, you use the formula: To find the number which fits in the middle square of an odd magic square, use the formula: These formulas enable Muhammad to easily construct magic squares of larger dimensions (“Muhammad”).
	massasoit.ath.cx /out/Math/muhammad.doc (1161 words)

	Prime Magic Squares
		The constant of this magic square is 111.
		The constant of this magic square is 177.
		The magic constants of the respective squares are 70681, 59807, 48933, 27185, 16311.
	www.geocities.com /CapeCanaveral/Launchpad/4057/primesqr.htm (2227 words)

	Ivars Peterson's MathTrek - Magic Tesseracts
		The traditional magic square consists of a set of integers arranged in the form of a square so that the numbers in each row, column, and diagonal add up to the same total.
		In four dimensions, the equivalent of a cube is a hypercube, or tesseract.
		The sum of the numbers in each of the rows, columns, pillars, and files (rows in a fourth spatial direction) and along the eight major quadragonals, which pass through the center and join opposite corners, is 524,296.
	www.maa.org /mathland/mathtrek_10_18_99.html (661 words)

	Magic Squares
		Magic is nothing more than our current understanding of technology and science, then Magic Squares may indeed be magic.
		Saturn Magic Square: the magic constant is 15 and the sum of all the numbers of the square is 45.
		Mercury Magic Square: the magic constant is 260, the sum of all the numbers of the square is 2080.
	www.halexandria.org /dward090.htm (2887 words)

	Magic Squares
		magic square whose only entry is the number 1.
		A technique known as the Siamese method can be used to generate magic squares with odd sizes (3, 5, 7, 9,...).
		In an 8 x 8 magic square, the diagonal numbers are 1, 4, 5, 8,..., 60, 61, and 64; so entry 1 is replaced with 64, 4 with 61, 5 with 60, and so on.
	home.att.net /~srschmitt/magicsquares.html (441 words)

	Odd Magic Square (Site not responding. Last check: 2007-10-21)
		Generally, magic squares are defined as sets of numbers arranged in the form of a square in such a manner that the sum of the numbers in any row, column, or diagonal is the same.
		A square that fails to be magic only because one or both of the main diagonal sums do not equal the magic constant is called a semimagic square.
		Odd Magic Square is a magic square which size (n) is the odd number.
	www.cybvic.org.mm /Resources?PageID=39 (278 words)

	Magic Cubes - Multiply
		Multiply magic cubes have the same basic requirements as the more familiar additive magic cubes, except that the magic constant is a product instead of a sum.
		This is a multiply magic cube so the magic constant is obtained by multiplying the four numbers in each line together.
		This is a regular magic square that produces a constant sum, but with the added property that all lines have a constant product when the numbers are multiplied instead of added.
	members.shaw.ca /hdhcubes/cube_multiply.htm (1244 words)

	More Magic Squares
		The constant of this new square is 666.
		This novelty magic square is known as the IXOHOXI magic square.
		This square is composed of the consecutive series of numbers from 1 to 81 and as is usual with pure magic squares, all rows, columns, and the two main diagonals sum to the constant 369.
	www.geocities.com /~harveyh/moremsqrs.htm (1287 words)

	Ivars Peterson's MathTrek - Perfect Magic Cubes
		A magic cube is a three-dimensional array of whole numbers, in which each row, column, and body diagonal (corner to corner, through the center) adds up to the same total.
		A perfect magic cube is one in which the diagonals of each vertical or horizontal slice through the cube also sum to the same value.
		As expected, the cube's magic constant is 315, and its central value is 63.
	www.maa.org /mathland/mathtrek_01_05_04.html (401 words)

	Perfect Magic Cubes
		In a (simple) magic cube the sums of the numbers in the diagonals may differ from S. According to John Hendricks the expression 'perfect' should be reserved for magic cubes that are pandiagonal and pantriagonal.
		The squares in the surface planes are not magic.
		Until September 1st, 2003 a diagonal magic cube of order 6 was not known and most magic cube experts thought that such a cube would not be possible.
	www.trump.de /magic-squares/magic-cubes/cubes-1.html (1226 words)

	[No title]
		A "near-magic" square is a 3x3 array such that the rows, columns, and one diagonal add to a magic constant.
		The second diagonal is not required to add to the magic constant.
		For near-magic squares generated by the Hillyer formulas, the magic constant will always be a perfect square - 21609 = 147^2.
	www.math.niu.edu /~rusin/known-math/99/magic_sq_EC (1034 words)

	Magic Cubes and Tesseracts
		A magic cube is defined as a cubical array such that all rows, columns, pillars, and four triagonals of the array sum to the same value (called the (magic) constant or the magic sum).
		Magic cubes are, as it were, three-dimensional magic squares.
		Similarly, a magic tesseract is a four-dimensional hypercube whose rows, columns, pillars, files, and eight quadragonals sum to the constant.
	homepage2.nifty.com /googol/magcube/en (554 words)

	Magic Squares 2
		Addition of magic squares does not result in another magic square, so they cannot be added.
		A magic square is composite if it is the product of two strictly smaller magic squares.
		A magic square is prime if it is not composite and is not the 'unit'
	home.att.net /~srschmitt/magicsquares2.html (273 words)

	ONDotnet.com: Refactoring with Visual Studio Macros
		Magic numbers are literal numbers in your application that are hard set, for instance you might have an age limit for a certain action, or perhaps a rate that is "set in stone".
		When our macro is complete, you can highlight the magic number you want to replace and execute the macro to have the number moved to a constant on the same class and the magic number replaced with the constant.
		When you select the number and run this macro, it replaces the magic number with the name of the constant and then inserts the constant, including the old value, at the top of the class.
	www.ondotnet.com /pub/a/dotnet/2005/06/20/macrorefactor.html (1937 words)

	[No title]
		>>The magic squares in question have the following properties: >>All rows & columns & both diagonals have the same sum (the usual >>condition); >>All broken diagonals have the same sum ("pandiagonal"); >>All 2-by-2 subsquares have the same sum; >>The sum of an entry and the entry n/2 diagonally away is constant.
		This is illustrated by the example, whose constant is 30.
		In general, a magic square is called pandiagonal if all its broken diagonals add up to the magic constant.
	www.math.niu.edu /~rusin/known-math/98/ollerenshaw (876 words)

	Magic Knight's Tour (Site not responding. Last check: 2007-10-21)
		A knight's tour of a chessboard is a sequence of moves by a knight such that each square of the board is visited exactly once.
		A magic square is a square array of numbers such that each row and column and the two main diagonals sum to the same number (the magic constant).
		Semi-magic knight's tours are known (in which the rows and columns sum to the same number, but the diagonals do not sum to that number).
	cage.rug.ac.be /~hvernaev/problems/Problem7.html (169 words)

	Magic Cubes-Introduction
		It included a new definition for the ‘perfect’ magic cube, which is applicable for magic hypercubes of any dimension.
		Magic cubes covers a wide field and I am sure everyone may not agree with everything I have said on these pages.
		A short description of the characteristics of pandiagonal and semi-pandiagonal magic squares and their counterpart in the pantriagonal and semi-pantriagonal magic cubes.
	members.shaw.ca /hdhcubes (2151 words)

	Magic Squares
		A magic square, of ANY size with an ODD number of squares on a side, can be constructed using this method.
		He constructed this "panmagic" square having magic constant 260.
		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)

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