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Topic: Magic tesseract

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	Magic square Summary
		In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, 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 Horton Conway) and the Strachey method for magic squares.
	www.bookrags.com /Magic_square (2733 words)

	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.
		The magic square figures in Greek writings dating from about 1300 BC were used by Arab astrologers in the ninth century when drawing up horoscopes.
	en.wikipedia.org /wiki/Magic_square (1488 words)

	Algorithms to make magic cubes and magic tesseracts
		A panmagic tesseract (namely, a pan-4-agonal or panquadragonal magic tesseract) can exist only if the order is divisible by 16, or the order is odd and higher than 5.
		It is unknown what condition is required and sufficient for the existence of strictly magic tesseracts (namely, 2,3,4-agonal magic tesseracts), but 2,3,4-agonal magic tesseracts exist for orders divisible by 4 and higher than 4, and for odd orders higher than 14, and cannot exist for order 3, 4, or 5.
		A strictly panmagic tesseracts (namely, a pan-2,3,4-agonal magic tesseract) can exist only if the order is divisible by 16, or the order is odd and higher than 16.
	homepage2.nifty.com /googol/magcube/en/algorithms.htm (976 words)

	Magic_square (Site not responding. Last check: 2007-11-06)
		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.
		Magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1.
		Yang Hui, in the 13th-century China, was one of the first mathematicians to study magic squares, or vertical and horizontal diagrams as they were called.
	www.apawn.com /search.php?title=Magic_square (1584 words)

	[No title]
		The Magic Hypercube is defined as a hypercube, regularlyy filled with integers [1,..,m
		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.
	home.wanadoo.nl /aaledewinkel/Encyclopedia/m/MagicHypercube.html (412 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 smallest perfect magic tesseract is of order 16 and is made up of 16 x 16 x 16 x 16 numbers.
	www.maa.org /mathland/mathtrek_10_18_99.html (661 words)

	[No title]
		Experimentation showed that the "half-pan' listing needed to be changed (digit changing was erraneously mistaken for main-diagonal permutation) Also I needed to correct the amount of {perfect} tesseract components to 1 and 3 (was 2 and 5).
		a tesseract defines as a sequence of m cubes
		a tesseract is a sequence of m cubes
	home.wanadoo.nl /aaledewinkel/Encyclopedia/x/XmlHypercubes.html (936 words)

	Magic Cubes and Tesseracts
		Added magic tesseracts of orders 8 and 12, which are both panmagic (that is, pan-4-agonal) and strictly magic (that is, 2,3,4-agonal), and renewed the page.
		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).
		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 (661 words)

	Magic hypercube -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		If, in addition, the numbers on every ((physics) the probability that a particular interaction (as capture or ionization) will take place between particles; measured in barns) cross section diagonal also sum up to the hypercube's magic number, the hypercube is called a perfect magic hypercube; otherwise, it is called a semiperfect magic hypercube.
		Five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by (Click link for more info and facts about J. Hendricks) J.
		From the proof follows a construction of magic hypercube.
	www.absoluteastronomy.com /encyclopedia/m/ma/magic_hypercube.htm (180 words)

	Magic tesseract - Wikipedia, the free encyclopedia
		The number n is called the order of the magic tesseract.
		If, in addition, the numbers on every cross section diagonal also sum up to the tesseract's magic constant, the tesseract is called a perfect magic tesseract; otherwise, it is called a semiperfect magic tesseract.
		This page was last modified 01:31, 15 April 2005.
	en.wikipedia.org /wiki/Semiperfect_magic_tesseract (97 words)

	John Hendricks
		As is common with composite magic squares, the magic sums of the order-5 squares themselves form an order-3 magic square with the constant 1695.
		This is the equivalent to the pandiagonal Magic Square.
		These are not requirements of a magic tesseract just as a magic cube is not required to have the planar square diagonals summing to 42.
	www.geocities.com /~harveyh/hendricks.htm (1917 words)

	Magic cubes and hypercubes - References
		D.N. Lehmer: On the enumeration of magic cubes
		Fucheng Zhu: On Nasik magic cubes and hypercubes
		A.Rogers, P.Loly: The inertia tensor of a magic cube
	fedu.ku.sk /~trenkler/Cube-Ref.html (1196 words)

	Magic CubeDefinitions
		Compact magic squares consist of 2x2 subsquares where the 4 cells sum to 4/m of S. Kanji Setsuda [2] extended the concept to magic cubes of order 4 where the four cells of all 2z2 squares, parallel to the sides of the cube sum to 130 (which is S for order 4 cubes).
		Composite, though, is an old term for magic squares that are composed from a group of small magic squares arranges as a magic square.
		the magic squares are all pandiagonal and the magic cubes are all pantriagonal and pandiagonal.
	members.shaw.ca /hdhcubes/cube_define.htm (4327 words)

	Magic Encyclopedia - Encyclopedia Shop (Site not responding. Last check: 2007-11-06)
		Encyclopedia with articles relating to magic squares, magic cubes, magic hypercubes and other objects.
		The Magic Encyclopedia Volume One … To an adventurer, the most prized treasure of all is magic.
		Encyclopedia: Magic (illusion) … took his stage name from Robert-Houdin and developed a range of stage magic tricks, many of them based on escapology.
	www.ecaseload.com /magic-encyclopedia.html (428 words)

	Alchemy, Magic, Incubation, Metatron, and Ancestors (Site not responding. Last check: 2007-11-06)
		It is called the Magic Cube because it is the definition of 3D.
		It is important to note that the Ancient Chinese wrote the I Ching according to this Magic Formulation.
		Magic and Alchemy start here, with the idea that there is another realm of conscious attainment.
	www.sangraal.com /library/dedicated.htm (1887 words)

	9-fold Higher Order Patterning of Tao Te Ching Insights
		The question was whether a magic square clustering, much favoured in that period in China, would enable new insights to be elicited from the resultant pattern.
		Just as the magic square total for the first 3x3 nested table is 15 (indicated above in Table 2 as 1:15), each other 3x3 nested table gives rise to its own total (indicated beneath it, eg 4:96, 9:231, and 2:42).
		Interesting patterns can be generated from magic squares when the numbers of the squares are replaced by symmetric symbols.
	www.laetusinpraesens.org /docs00s/taote7.php (5765 words)

	Tesseract
		To see how to construct a Tesseract - a 4 dimensional cube (often also, a hypercube) - press the Start button.
		When finished, you'll be able to rotate the tesseract with sliders or by dragging the mouse.
		Ax + By + Cz + Dh = E. (Throughout, the fourth coordinate is denoted by h or H as a reminder that we deal with a hyperspace.)
	www.cut-the-knot.com /Curriculum/Geometry/Tesseract.shtml (146 words)

	Tesseracts in RPGs
		All images are repeats of the same representation of a tesseract, but each one highlights a different one of the 8 cells.
		If the tesseract is large enough, the upward curving would be gradual and you wouldn't have any problems with sudden gravity shifts like you would anywhere else.
		Some crazed wizard, god, pantheon, or magically talented race decided to construct the tesseract for a variety of reasons: as a plaything, experiment, prison, or refuge come immediately to mind.
	members.tripod.com /~hawk_wind/worlds/Tess.html (3530 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 magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube.
		This means that the magic squares are all pandiagonal and the magic cubes are all pantriagonal and pandiagonal.
	laetusinpraesens.org /docs00s/taote4.php (3509 words)

	First Adventure : December 2nd, 2000
		It is clearly magical, but fails to radiate magic, just as the ring and the mysterious tome did.
		The ancient magic has two sources, the Sword of Ashrek (which is the obelisk) and the Pit of Sollux.
		Using magic, he is able to establish that the mountain is on the 263
	www.tesseract.org /harry/world/campaign_summary.html (1988 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 magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube.
		This means that the magic squares are all pandiagonal and the magic cubes are all pantriagonal and pandiagonal.
	www.laetusinpraesens.org /docs00s/taote4.php (3478 words)

	Magic the Gathering expansion? - Wizards Community
		The Magic Developers are against diluting "brand identity" and many in the DandD community would freak out if a magic expansion (or a DandD expansion for magic) happened.
		A d20 Magic supplement not to be meant to use with DandD might be fun, but I want both brands which I love to remain separate.
		Magic and Dungeons and Dragons and Wargames tend to have different fans, but they have a lot of overlap.
	boards1.wizards.com /showthread.php?goto=lastpost&t=715428 (2108 words)

	Self-similar Magic Squares
		Whether these magic squares are semi-pandiagonal or simple seems to have no bearing on whether a horizontal or vertical reflection is required to match the complement to the original.
		Because this is an associated magic square, the complementary square must be both horizontally and vertically reflected to match the original.
		Any non-associated magic squares that have complementary pairs that are symmetric across either the horizontal or the vertical center line produce self-similar copies that are either horizontally or vertically reflections of themselves.
	www.geocities.com /~harveyh/self-similar.htm (1436 words)

	magic number spirals
		The pattern formed by the squares and triangles themselves also fits into the form of a tesseract (or a fourth-dimensional cube, or hypercube).
		Here is what the spirals extrapolated from the Pythagorean squares look like integrated with the larger tesseract pattern into which the squares fit.
		The tesseract pattern will be discussed in more depth in the next thread following this.
	home.comcast.net /~benpadiah/phi_over_pi.html (643 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-11-06)
		In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant.
		Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist..
		The smallest known perfect magic tesseract is of order 16; its magic constant is 524296, and it w..
	pardus.info /browse.php?title=P/PE/PER (10984 words)

	Inlaid Magic Cubes
		A coordinated definition of the main types of magic cubes, that is consistent and extends to all dimensions of magic hypercubes.
		I call this a versatile magic cube because it may be easily changed to a different cube by changes to the components.
		The magic sum for the sixth-order tesseract is 3891 and the magic sum for the inner magic sub-tesseract revealed by the red numbers, is 1824.
	members.shaw.ca /hdhcubes/cube_inlaid.htm (2684 words)

	EDGE and Tesseract Books
		Stealing Magic is both appealing and amusing, and belongs in everyone's fantasy collection.
		If you haven’t encountered her yet, Stealing Magic is an excellent place to start.
		Stealing Magic is bound like an old Ace double--one side for the Terazin stories, and one for the Magdalene stories--making for a great bi-directional read, with double cover art by David Willicome that's both handsome and suitable to the stories."
	www.edgewebsite.com /books/stealingmagic/sm-catalog.html (795 words)

	Books : Galveston (Site not responding. Last check: 2007-11-06)
		The clever conceit of Galveston is that magical realism, made literal, can become the basis for science-fiction / fantasy.
		Magic demands no credibility because it is firmly beyond question.
		In a not-so-distant future, on the island of Galveston, Texas, civilization is slowly slipping away and decaying, and no amount of plaster can fix the crumbling marble walls.
	www.arabiadirectory.com /0441008003/Galveston.shtml (442 words)

	The Tesseract - a 4-dimensional cube
		In anticipation of MAM 2000, a remark by A.
		A 3-dimensional cube is bounded by 6 2-dimensional squares.
		A 4-dimensional tesseract is bounded by 8 3-dimensional cubes.
	www.cut-the-knot.org /ctk/Tesseract.shtml (1271 words)

	YouthLink - If You Love Harry Potter Booklist (Site not responding. Last check: 2007-11-06)
		Lizzie is convinced of her own magical powers, and all three Sharp children soon become ridiculously entangled in a web of secrets, conspiracies, and misunderstanding.
		He claims to have been blown off course, and goes on to tell them that there is such a thing as a "tesseract," which, if you didn't know, is a wrinkle in time.
		Harry Crewe, bored with her sheltered life in the remote orange-growing colony of Daria, discovers magic in herself when she is kidnapped by a native king with mysterious powers.
	www.futuris.net /ferg/youth_link/kidol/booklists/harrypotter.htm (688 words)

	Review of Tanya Huff's Stealing Magic
		Stealing Magic is charming, funny, and once again proves that Huff has no regard for the conventions and boundaries of genre.
		Adar is the king's wizard and he has a nefarious plan, of which Magdelene is unaware, to steal her power.
		All of his malevolence and cunning are no match for Magdelene's innocent fascination with magic and her raw power.
	www.challengingdestiny.com /reviews/stealingmagic.htm (839 words)

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