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Topic: Multimagic cube

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Trimagic cube

Bimagic cube

Trimagic square

Bimagic square

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	cube (Site not responding. Last check: 2007-11-05)
		The cube is a special kind of square prism, of rectangular parallelepiped and of triangular trapezohedron, and is dual to the octahedron.
		In arithmetic and algebra, the cube of a number n is its third power — the result of multiplying it by itself two times: This is also the volume formula for a geometric cube of side length n, giving rise to the name.
		A cube opened out gives a cross of six squares, four in the vertical line and three in the horizontal, one square being common to both, which is an emblem of the human being with his spiritual and material nature meeting at the intersection.
	www.vocamania.com /cube.aspx (1740 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 diagonals are correct in all 16 horizontal planes and all 16 vertical planes parallel to the sides of the cubes.
		So a magic cube remaining magic when all its numbers are squared, and again remaining magic when all its numbers are cubed.
	members.shaw.ca /hdhcubes/cube_multimagic.htm (2270 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)

	Magic Square Encyclopedia Article @ Occasioned.org (Site not responding. Last check: 2007-11-05)
		If not only the main diagonals but also the broken diagonals sum to the magic constant, the result is a panmagic square.
		If raising each number to certain powers yields another magic square, the result is a bimagic, a trimagic, or, in general, a multimagic square.
		Going up in dimension results in magic cubes, magic tesseracts and other magic hypercubes.
	www.occasioned.org /encyclopedia/Magic_square (2463 words)

	Trimagic cube - Wikipedia, the free encyclopedia
		The first trimagic cube was found by C. Boyer on February 1, 2003 and is of order 64.
		This cube and its square are perfect, while its cube is only semiperfect.
		This cube, its square, and its cube are all perfect.
	en.wikipedia.org /wiki/Trimagic_cube (108 words)

	9-fold Higher Order Patterning of Tao Te Ching Insights
		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 pandiagonal cube is a perfect or semiperfect magic cube which is magic not only along the main space diagonals, but also on the broken space diagonals [more].
		If the associated cube (or other dimension of hypercube) is an odd order, then the center of the cube is a cell containing one half the sum of the first and last number in the series.
	www.laetusinpraesens.org /docs00s/taote4.php (3475 words)

	Arnoux cube
		The second of Boyer’s cubes contains 48 simple magic squares and because all planar squares have diagonals that sum correctly, the tube is classed as ‘diagonal’ magic.
		He probably did not construct the actual cube, because he claimed the cube was associated (which it is not).
		This cube is repeated 27 times, using the consecutive numbers from 1 to 3375 to form the order 15 cube.
	members.shaw.ca /hdhcubes/cube_big.htm (2364 words)

	magic series - Multimagic series
		In multimagic series additionally the sums of certain powers of the numbers have to equal constant values.
		This discovery and all about multimagic series is described at the famous website www.multimagie.com (external link) of Christian Boyer.
		This enabled me to determine the number of bimagic series for cubes of the orders 9 and 10 in October 2005.
	www.trump.de /magic-squares/magic-series/multi.htm (531 words)

	Magic Squares
		A magic square is said to be trimagic when, in addition to the requirement for a bimagic square, the square formed by replacing every number by its cube is also a magic square.
		The sum of the squares of the numbers in each row, each column and both diagonals is equal to 11 201 200.
		The sum of the cubes of the numbers in each row, each column and both diagonals is equal to 8 606 720 000.
	www.magic-squares.de /gallery/multimagic/example31.html (156 words)

	Table Topics Cube - Table Topics Cube (Site not responding. Last check: 2007-11-05)
		Registration is not required to view current topics on the Bulletin Board; however, if you wish to post a new topic or reply to an existing topic registration is required.
		Build a second cube, using the view as the basis for the cube's fact table...
		floating around in a cube that are attracted to each...
	www.table-furniture-guide.com /table-topics-cube.html (1072 words)

	Multimagic Squares
		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).
		More are available on his Web site (called Multimagic Squares.), including files of the two squares that may be downloaded.
	www.geocities.com /~harveyh/multimagic.htm (762 words)

	Magic Square :: Recreations
		Magic Cubes and Tesseracts - Examples, original works, algorithms, and theorems on magic cubes, tesseracts, and hypercubes.
		Magic Squares and Hyper Cubes - Includes Java Applet and source code of square and hyper cube generator.
		Skeleton Magic Squares - Demonstrates methods and algorithms for squares and cubes.
	science.gourt.com /Math/Recreations/Magic-Square.html (1097 words)

	MedMark.org Category: /Science/Math/Recreations/Magic_Square
		Magic Cubes - The site presents a program for finding all possible order 3 cubes, executable and source included.
		Multimagic Squares - Squares that remain magic after entries are raised to various powers.
		Program on Hyper Magic Cubes - Downloadable program displays random hyper cubes of given order and dimension.
	www.medmark.org /odp.php?browse=/Science/Math/Recreations/Magic_Square (979 words)

	I O Magic - Information
		also cube Trimagic cube Magic square Bimagic a square that remains even if a magic square is 4 square, of 5 magic square, of 4 magic square of 5 square, of also cube Multimagic i o magic.
		a hypercube is of square s, cube s and magic tesseract s, called constant of a magic hypercube consists has magic number :M s number, the perfect hypercube ; semiperfect hypercube.
		The library, that create hypercubes of on cubes and hdhcubes Cubes Introduction category: squares with, and fairy can lose their magic.
	home.tiscali.de /onlineinfo/i-o-magic.html (418 words)

	Philosophical Fortnights: Philosophy of Mathematics Archives
		Carrés multimagiques (multimagic squares, multimagischen Quadrate) are magic squares such that if every number in the square is replaced its square (cube, etc.) the result is also a magic square.
		A magic square is an n × n array of natural numbers (in a “normal” magic square, the consecutive numbers from 1 to n2) for which every row, column, and diagonal adds up to the same number.
		There are also magic cubes, for which every line of numbers between two faces or vertices (and, in a perfect magic cube, every line of numbers between two edges)—every “row, column, pillar, and space diagonal”—adds up to the same number.
	tlonuqbar.typepad.com /phfn/philosophy_of_mathematics/index.html (2376 words)

	Trimagic Cube -- from Wolfram MathWorld
		A trimagic cube is a magic cube that remains magic when all its numbers are both squared and cubed.
		This cube, its square, and its cube are all
		Weisstein, Eric W. "Trimagic Cube." From MathWorld--A Wolfram Web Resource.
	mathworld.wolfram.com /TrimagicCube.html (92 words)

	Magic cubes and hypercubes - References
		Miklós Bóna: Sur l'énumération des cubes magiques (On the number of the magic cubes) (French)
		Magic figures: Magic squares, magic triangles, magic cubes, and magic hypercubes
		Magic squares and cubes in school: MA thesis by Katarína Pavlíková (Slovak)
	fedu.ku.sk /~trenkler/Cube-Ref.html (1179 words)

	The Zen of Magic Squares, Circles, and Stars:
		Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization?
		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)

	Math Trek: Perfect Magic Cubes, Science News Online, Jan. 3, 2004 (Site not responding. Last check: 2007-11-05)
		Math Trek: Perfect Magic Cubes, Science News Online, Jan. 3, 2004
		Christian Boyer has a Web site devoted to multimagic squares at http://www.multimagie.com/indexengl.htm.
		A collection of Ivars Peterson's early MathTrek articles, updated and illustrated, is now available as the Mathematical Association of America (MAA) book Mathematical Treks: From Surreal Numbers to Magic Circles.
	www.sciencenews.org /20040103/mathtrek.asp (490 words)

	The Prime Puzzles and Problems Connection (Site not responding. Last check: 2007-11-05)
		Numbers that are equal to the sum of cubes of its third parts (as strings)
		Sum of Cubes equal to Square of Sum
		The unit and the sum of three signed prime-cubes
	www.primepuzzles.net /puzzles (574 words)

	Science Directory, Technology, Biology, Agriculture, Energy - Mathematics > Recreations
		Examples : group theory, dynamical systems theory, geometry or number theory.
		Topics include Flexagon, Soma Cube, Pentominos, Cube-it, Rubik's Cube, Froebel's Star, Tangram, House of Santa Claus, Chronogram, Numeric Palindromes, Latticework of Letters.
		Magic squares which remain magic after their entries are raised to various powers.
	www.sciencedirectory.info /mathematics/recreations (188 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		%Y A019756 Adjacent sequences: A019753 A019754 A019755 this_sequence A019757 A019758 A019759 %Y A019756 Sequence in context: A016697 A086466 A021703 this_sequence A010650 A011091 A120362 %K A019756 nonn,cons %O A019756 0,2 %A A019756 njas %I A010650 %S A010650 4,3,0,8,8,6,9,3,8,0,0,6,3,7,6,7,4,4,3,5,1,8,5,8,7,1,3,3,0,3,8,7,0, %T A010650 0,9,9,0,5,1,8,6,8,9,8,8,4,3,8,4,2,1,7,1,6,4,9,7,8,4,7,1,0,1,2,6,9, %U A010650 2,8,2,2,2,1,3,2,9,6,6,8,1,6,0,0,3,7,0,8,8,3,0,0,7,0,8,6,4,8,6,5,5 %N A010650 Decimal expansion of cube root of 80.
		%K A123683 nonn,tabf,new %O A123683 1,5 %A A123683 Alford Arnold (Alford1940(AT)aol.com), Oct 06 2006, Oct 19 2006 %I A010306 %S A010306 4,3,1,2,120,7,1,45,3,2,6,1,4,149,1,1,1,9,2,4,2,2,23,2, %T A010306 1,1,1,5,49,4,1,3,1,2,1,3,1,1,1,5,1,1,9,1,4,2,3,2,2,1,2, %U A010306 1,12,1,2,79,5,22,3,1,12,2,14,1,6,8,1,2,1,1,2,1,1,4,1,2 %N A010306 Continued fraction for cube root of 78.
		%Y A021702 Adjacent sequences: A021699 A021700 A021701 this_sequence A021703 A021704 A021705 %Y A021702 Sequence in context: A076576 A110631 A071890 this_sequence A010651 A074066 A067016 %K A021702 nonn,cons %O A021702 0,4 %A A021702 njas %I A010651 %S A010651 4,3,2,6,7,4,8,7,1,0,9,2,2,2,2,5,1,4,6,9,6,4,9,1,4,9,3,2,3,4,0,3,2, %T A010651 8,7,6,5,1,7,5,6,0,7,7,6,0,4,9,8,0,5,1,7,3,2,6,3,9,2,4,8,5,8,3,6,2, %U A010651 5,0,6,2,7,9,0,4,8,9,9,9,2,0,1,9,5,6,4,2,6,6,4,3,9,1,1,6,9,3,5,7,7 %N A010651 Decimal expansion of cube root of 81.
	www.research.att.com /~njas/sequences/eisBTfry00065.txt (6310 words)

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