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Topic: Trimagic square

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Trimagic cube

Bimagic square

Bimagic cube

Multimagic square

Antimagic square

Magic cube

Magic constant

Multimagic cube

Panmagic square

Magic star

Diabolic square

Magic tesseract

Heterosquare

LUX method for magic squares

Prime reciprocal magic square

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	Magic square (Site not responding. Last check: 2007-11-06)
		In mathematics, magic squares consist of a number of integer s 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.
		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.
	www.serebella.com /encyclopedia/article-Magic_square.html (1753 words)

	Magic square (Site not responding. Last check: 2007-11-06)
		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.
		The magic sum of the square is 33, the age of Jesus at the time of the Passion.
		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)

	Square \| TutorGig.co.uk Encyclopedia (Site not responding. Last check: 2007-11-06)
		Hanover Square, is a square in Queensbury, Bradford, BD1, England Hanover Square, Herne Bay, Canterbury, Kent Canterbury, CT6, England Hanover Square, Macworth, Derby, DE22, England Hanover Square
		A square foot is by definition the area enclosed by a square geometry square with sides each 1 foot unit of length foot long.
		Stanley Bagshaw and the Mafeking Square Cheese Robbery
	www.tutorgig.co.uk /encyclopedia/sencyclo.jsp?keywords=Square (523 words)

	MULTIMAGIE.COM - Story of the smallest trimagic square
		A multimagic square is a magic square remaining magic when all its numbers are raised to various powers (squared, cubed, ).
		We discussed the question whether there is a smaller trimagic square than the one found by Benson which is of order 32 (which means 32 rows and 32 columns).
		After some hours, exactly with the 88th semi-trimagic square, a trimagic diagonal could be constructed and — for reasons of symmetry — the second diagonal was automatically trimagic, too.
	cboyer.club.fr /multimagie/English/Tri12Story.htm (1885 words)

	Multimagic Cubes
		The sum is 130 in the 16 columns, 16 rows, 16 pillars, and in the 4 main diagonals of the cube.
		The 4096 rows, 4096 columns and 4096 pillars are trimagic.
		A trimagic cube with all its trimagic diagonals (and of course always trimagic rows, columns, pillars and triagonals) have been constructed.
	members.shaw.ca /hdhcubes/cube_multimagic.htm (2277 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The one with the smallest permutation along the main diagonal I named the "Least Diagonal Representative", any derived trimagic square will have a higher permutation of the same numbers along the main diagonal.
		Thus defined the squares are best listed by the "Least Diagonal Representative" (LDR) and derive a particular square within the thus defined "family" as LDR
		The excell trimagic order 12 spreadsheet gives access to all related trimagic squares, just mention the given permutation will be enough to alert attention to a particular square within these 23040 squares
	home.wanadoo.nl /aaledewinkel/Encyclopedia/DataBase/TrimagicSquaresOrder12.html (477 words)

	Play in the sunshine
		Trimagic squares seem to require the dimension to be at least 32.
		It appears that magical squares can have still other magical properties, such as magicalness of all generalized diagonals (a generalized diagonal is obtained by continuing a diagonal at the other side).
		View for example this picture of a trimagic square of dimension 32, one of the many gems to be found on the site.
	micans.org /stijn/topics/sunshine.html (612 words)

	Square kilometre in TutorGig Encyclopedia
		Square kilometre United States U.S. spelling Square kilometer, symbol km, is an SI unit of surface...
		Square megametre symbol Mm sup 2 sup is an SI unit of surface area.
		A satanic square is a magic square that remains magic after all its numbers are raised to a specific fixed power.
	www.tutorgig.com /es/Square+kilometre (1031 words)

	magic square
		See live article Magic square 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.
		See live article Multimagic square 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 iff it is 2-multimagic, and trimagic iff it is 3-multimagic.
		Basically, it's a magic square that remains magic after all its numbers are raised to a specific (fixed) power.
	www.theorderofperdition.com /dark/magic+square (942 words)

	Definition of square (Site not responding. Last check: 2007-11-06)
		A board is often [[millingmilled]] [[four square ]] in preparation for using it in building furnitu...
		1: '''Kendall Square ''' is a neighborhood in [[Cambridge, Massachusett...
		There are no antimagic square s of size $2 \times 2$ or $3 \t...$
	www.wordiq.com /dictionary/square.html (732 words)

	[No title]
		squares obtained by this method (the first 16 are listed in sampleset 2 resp 3), the input-
		the latin squares are calculated using coordinates [0..m-1] in the first and [1..m] in the
		Square multiplication is a way to combine two square into one by a method simular to
	home.wanadoo.nl /aaledewinkel/Encyclopedia/DataBase/GeneralSpreadsheets.html (1213 words)

	Glossary
		A pandiagonal magic square may be converted to another by simply moving one row or column to the opposite side of the square.
		The principle reversible square is defined as that one containing 1 and 2 as the first two numbers in the first row and all its rows and columns in, respectively, sequences of integers in ascending order.
		Any magic square in which the complementary pairs are symmetric across either the horizontal or the vertical center line of the square is self-similar.
	www.geocities.com /~harveyh/glossary.htm (8579 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.
		From any magic square, there are always a family of additional squares that may be obtained by various transformations.
	www.geocities.com /~harveyh/multimagic.htm (764 words)

	MULTIMAGIE.COM - Multimagic series
		Here is a summary of the number of multimagic series for each order from 3 to 13, some of these lists being downloadable as Excel files, from 28Kb to 800Kb each.
		For the order 12, the numbers of the trimagic, tetramagic and pentamagic series are kindly communicated by Walter Trump, Germany.
		The bimagic, trimagic, tetramagic and pentamagic series are referenced respectively under the numbers A052457, A052458, A090037 and A106646 in the Neil Sloane's Encyclopedia of Integer Sequences, ATandT Research.
	cboyer.club.fr /multimagie/English/Series.htm (388 words)

	Trimagic square - Wikipedia, the free encyclopedia
		In mathematics, a trimagic square is a magic square that also remains magic if all of the numbers it contains are squared or cubed.
		Trimagic squares of orders 12, 32, 64, 81 and 128 have been discovered so far; the only known trimagic square of order 12, given below, was found in June 2002 by German mathematician Walter Trump.
		This page was last modified 00:56, 30 June 2005.
	en.wikipedia.org /wiki/Trimagic_square (85 words)

	Magic square (Site not responding. Last check: 2007-11-06)
		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.
		When a move would leave the square, it is wrapped around to the first row or last column, respectively.
		Generates all 5x5 magic squares, entries may be prescribed ( http://www.faust.fr.bw.schule.de/mhb/backtrack/mq5/index.html)
	www.mywiseowl.com /articles/Magic_square (1417 words)

	Magic Cubes - The Road to Perfect
		All 6 diagonal square arrays are simple magic (3 of the six have all the pandiagonals in one direction correct).
		All 24 planar squares are pandiagonal magic as are also the 6 oblique squares and the seven broken squares parallel to each of these[1][5] for a total of 72 pandiagonal magic squares.
		It is one of the seven pandiagonal magic squares parallel to the oblique square from the upper left to lower right sides of the cube.
	members.shaw.ca /hdhcubes/cube_perfect-2.htm (5492 words)

	magic squares
		The Zen of Magic Squares, Circles, and Sta...
		Trimagic squares of orders 12, 32, 64, 81 and 128 have been discovered so far;...
		Extended Euclidean algorithm Table of divisors Prime number Table of prime factors Factorization RSA number Fundamental theorem of arithmetic Square -free Perfect square Dyadic fraction Farey sequence Ford circle Modular arithmetic Linear congruence theorem Method of successive substitution Chinese remainder theorem...
	www.theorderofperdition.com /dark/magic+squares (942 words)

	MULTIMAGIE.COM - Magic squares of squares
		Each multimagic (bimagic, trimagic, ) square is a “ magic square of squares ” when its numbers are squared.
		But a “ magic square of squares ” is rarely a multimagic square because it is probably not magic when its numbers are not squared.
		3 semi-magic square of squares by Edouard Lucas in 1876
	cboyer.club.fr /multimagie/English/SquaresOfSquares.htm (1414 words)

	Trimagic square - TheBestLinks.com - Germany, Mathematics, Mathematician, Magic square, ...
		Trimagic square - TheBestLinks.com - Germany, Mathematics, Mathematician, Magic square,...
		Trimagic square, Germany, Mathematics, Mathematician, Magic square, June 2002...
		You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
	www.thebestlinks.com /Trimagic_square.html (126 words)

	Monster Cubes
		Christian has a very informative site where he discusses multimagic cubes (and squares) but his material on these large cubes is not presented in quite this way.
		Gaston Tarry, inventor of the "tetramagic" term, was the first person to have constructed a trimagic square, in 1905.
		In his cases all planar diagonals sum correctly, so all planar arrays are simple magic squares.
	members.shaw.ca /hdhcubes/boyer-monster.htm (986 words)

	Science Fair Projects - Bimagic square
		In mathematics, a bimagic square is a magic square that also remains magic if all of the numbers it contains are squared.
		Hendricks was able to show in 1998 that no bimagic square of order 3 exists, save for the trivial bimagic square containing the same number nine times.
		Aale de Winkel's listing of all 80 bimagic squares of order 8.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Bimagic_square (279 words)

	Bibliography (Site not responding. Last check: 2007-11-06)
		This book is mostly about magic squares, but includes discussions and examples of magic cubes and magic stars.
		Note that Gardner erroneously stated that all 5 x 5 magic squares with 13 in the center are associated.
		Pages 736 to 753 is about diabolic (perfect) magic cubes and points out there are 3 m diabolic magic squares parallel to the faces of the cubes and 6 m diabolic magic squares parallel to each of the diagonal planes.
	www.geocities.com /~harveyh/bibliography.htm (3882 words)

	The Zen of Magic Squares, Circles, and Stars:
		Whether you're seeking an introduction to magic squares, an in-depth study, some historical information, or just some enjoyable magic figure problems, tricks, properties, or novelties-this book is for you.
		Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes.
		The new multimagic record is a pentamagic square (5-multimagic) built in 2001 by André Viricel and Christian Boyer.
	sprott.physics.wisc.edu /pickover/zenad.html (1146 words)

	Tri Magic Square (Site not responding. Last check: 2007-11-06)
		The following array of numbers is the world's smallest known trimagic square.
		The sum of its rows, columns, and both diagonals are each 9,520.
		If you square all the numbers, then the sums are 8,228,000.
	www.pen.k12.va.us /Div/Winchester/jhhs/math/puzzles/trimagic.html (46 words)

	Magic Squares Links
		Farrar, Mark S. Magic Squares from the viewpoint of a magicican
		Grogono, Alan W. Theory of pandiagonal Magic Squares
		A large site about Magic Squares: a great database, algorithms, mathematical background, history and a lot of links.
	www.magic-squares.de /general/additional/links.html (129 words)

	Magic Encyclopedia index m magic square, magic cube, magic tesseract, magic hypercube,
		Magic Encyclopedia index m magic square, magic cube, magic tesseract, magic hypercube,
		Harvey Heinz site on "magic stars squares and other subjects"
		(A.Adler's) Magic Squares: 'Multiplication' in a new context
	home.wanadoo.nl /aaledewinkel/Encyclopedia/m/m.html (204 words)

	Claremont, Minnesota bei eLexi - das Onlinelexikon (Site not responding. Last check: 2007-11-06)
		The pipeline will transport natural gas, from the Caspian Sea, through
		Trimagic squares of orders 12, 32, 64, 81 and 128 have been
		The Treaty of Kuçuk Kainarji was signed in 1774 between Russia and the Ottoman Empire after the Ottoman Empire was defeated in a Russo-Turkish War.
	www.elexi.de /en/c/cl/claremont__minnesota.html (574 words)

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