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	Impossible cube - Wikipedia, the free encyclopedia
		The impossible cube or irrational cube is an impossible object that draws upon the ambiguity present in a Necker cube illustration.
		An impossible cube is usually rendered as a Necker cube in which the edges are apparently solid beams.
		A doctored photograph purporting to be of an impossible cube was published in the June 1966 issue of Scientific American, where it was called a "Freemish Crate".
	www.wikipedia.org /wiki/Impossible_cube (264 words)

	Impossible cube: Definition and Links by Encyclopedian.com - All about Impossible cube
		The impossible cube or irrational cube is an impossible object.
		A doctored photograph purporting to be of an impossible cube was published in the June 1966 number of Scientific American, where it was called a "Freemish Crate".
		The Necker cube is an ambiguous picture that consists of a wire-frame drawing of a cube in isometric perspective.
	www.encyclopedian.com /im/Impossible-cube.html (198 words)

	Impossible cube (Site not responding. Last check: 2007-09-20)
		Escher 's lithograph Belvedere, the figure of a boyseated at the foot of the building is holding an impossible cube and the entire picture is based on the same principle that makesthe impossible cube.
		A doctored photograph purporting to be of an impossible cube was published in the June 1966 number of Scientific American, whereit was called a "Freemish Crate".
		The Necker cube is an ambiguous picture that consists of a wire-framedrawing of a cube in isometric perspective.
	www.therfcc.org /impossible-cube-313090.html (218 words)

	Impossible object - Wikipedia, the free encyclopedia
		An impossible object is an object that cannot exist according to the known laws of nature, but has a description or representation suggesting, at first sight, that it can.
		The undecidability of these figures invariably rests on them being interpreted as two-dimensional projections of what would be an impossible higher-dimensional object.
		In the Star Trek: The Next Generation episode "I, Borg", a plan was made to destroy the entire race of Borg – malevolent cybernetic aliens whose minds were interconnected – by showing one of the borg a picture of a highly-complex impossible object.
	en.wikipedia.org /wiki/Impossible_object (215 words)

	Necker cube - Wikipedia, the free encyclopedia
		It is a wire-frame drawing of a cube in isometric perspective, which means that parallel edges of the cube are drawn as parallel lines in the picture.
		The Necker Cube is sometimes used to test computer models of the human visual system to see if they can arrive at consistent interpretations of the image the same way humans do.
		A cube whose edges cross in an inconsistent way is called an impossible object, specifically an impossible cube.
	en.wikipedia.org /wiki/Necker_cube (475 words)

	Impossible Figures in Perceptual Psychology
		Interposition is used in many impossible figures to suggest that one part of an object is in front of another.
		Gregory discusses a similar case with the Penrose impossible triangle, in his essay, "The Confounded Eye." The Penrose impossible triangle is a physical object which appears to be impossible.
		The impossibility arises from the assumption that the triangle lies in a plane.
	www.fink.com /papers/impossible.html (3265 words)

	Encyclopedia: Impossible cube
		Two famous undecidable figures, the Penrose triangle and devils pitchfork An impossible object is an object that cannot exist according to the known laws of nature, but has a description or representation suggesting, at first sight, that it can.
		A so-called impossible cube seen from an angle that makes the non-impossibility of the object apparent.
		The Penrose triangle The Penrose triangle, also known as the tribar is an impossible object.
	www.nationmaster.com /encyclopedia/Impossible-cube (710 words)

	Necker cube (Site not responding. Last check: 2007-09-20)
		The Necker Cube is an ambiguous line It is a wire-frame drawing of a in isometric perspective which means that parallel of the cube are drawn as parallel in the picture.
		The Cube is sometimes used to test computer of the human visual system to see they can arrive at consistent interpretations of image the same way humans do.
		A cube whose edges in an inconsistent way is called an impossible cube.
	www.freeglossary.com /Necker_cube_illusion (378 words)

	Impossible Figures (Site not responding. Last check: 2007-09-20)
		"Impossible" objects are those that are impossible in three dimensions, but can be created in two dimensions to make an illusion in three dimensions.
		The cube displayed on the stamp below is used by M. Escher in both Man with Cuboid and Belvedere, from 1958.
		In Belvedere the structure also is based on the impossible cube.
	sio.midco.net /danstopicalstamps/impossible.htm (80 words)

	Dynamics of a Floating Object
		The cube was chosen because it simplifies many of the calculations required in modeling its interaction with a liquid.
		Because the cube is always upright, the amount of submersion can be approximated by evaluating the height of the water surface at each of vertically oriented edges of the cube.
		The density of water is fixed at 1000 kilograms per cubic meter and the cube's cross-sectional area is approximated by the area of one of the cube's faces.
	www.cs.ubc.ca /spider/van/cpsc526/Vjan2003/projects/report.html (1611 words)

	basic intro
		Just as a cube casts different shaped two dimensional shadows as it is rotated in three dimensional space, so, too, does the hypercube cast different shaped three dimensional shadows as it rotates in four-space.
		The eighth cube is simply hidden within this form of the hypercross, between the six surrounding cubes and the central seventh.
		This type of impossible cube was discovered, along with a similar impossible triangle, in the 20th century by mathematician Roger Penrose.
	home.comcast.net /~benpadiah/intro.html (1020 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.
		(In a non-normal cube the integers are not consecutive.)
		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)

	Impossible cube - Encyclopedia, History, Geography and Biography
		This apparent solidity gives the impossible cube greater visual ambiguity than the Necker cube, which is less likely to be perceived as an impossible object.
		Escher's lithograph Belvedere, the figure of a boy seated at the foot of the building is holding an impossible cube; the rest of the scene is based on the same principle that makes the impossible cube.
		This encyclopedia, history, geography and biography article about Impossible cube contains research on
	www.arikah.net /encyclopedia/Impossible_cube (264 words)

	Image:Impossible cube illusion angle.png - Wikipedia, the free encyclopedia
		A so-called impossible cube seen from an angle which produces an illusion of impossibility.
		This picture/multimedia file is now available on Wikimedia Commons as Image:Impossible cube illusion angle.png.
		473x480 (5539 bytes) (A so-called impossible cube seen from an angle which produces an illusion of impossibility.
	www.wikipedia.org /wiki/Image:Impossible_cube_illusion_angle.png (191 words)

	Unusual Magic Cubes
		In this paper he gave examples of cubes consisting of a number in each cell such that each row, column, and pillar consisted of an m digit number that was a reversible prime.
		The impossible cube uses the numbers 1 to 43 in 8 lines of 5, 2 lines of 7 and 1 line of 3.
		The cube consists of 27 smaller cubes which, in the initial configuration, are colored so that the 6 faces of the large cube are colored in 6 distinct colors.
	members.shaw.ca /hdhcubes/cube_unusual.htm (4258 words)

	Trisecting the Angle
		It is impossible to represent the square root of two as a fraction of whole numbers.
		Actually this proof is related to the proofs that trisecting the angle, doubling the cube and squaring the circle are impossible.
		Doubling the cube amounts to finding the cube root of two, that is, also solving a cubic equation.
	www.uwgb.edu /dutchs/PSEUDOSC/trisect.HTM (4996 words)

	CubeOwner Forums -> For those with a fried dc board from the d-800 PL
		My frustration is mounting, as I'm sure anybody's would if they had their beloved Cube in the shop for almost a month with no hope of return in the near future.
		Apparently, there were 4 Cube owners to whom this happened and it would be nice to hear about their experiences.
		I was told by powerlogix not to send my cube in but that they would send me a modified dc-dc card but did not give me a time frame.
	www.cubeowner.com /forums/index.php?showtopic=703 (3939 words)

	Impossible Objects - Amazing Art (Site not responding. Last check: 2007-09-20)
		Very nice variation on the impossible cube, especially the way how two cubes are in the middle of two sides.
		A woman is looking at an impossible wooden box with a puzzled expression on her face.
		Three impossible things : two books become three books, the vase is in front of the green jar but behind the books, and the red pot has a strange bottom.
	members.lycos.nl /amazingart/E/42.html (685 words)

	Cube impossible (Site not responding. Last check: 2007-09-20)
		Le cube impossible ou cube irrationel est un objet impossible.
		Le cube est dessinÃ© avec des poutres solides, qui se croisent de faÃ§on inconsistente.
		Le cube de Necker est sur la gauche, le cube impossible sur ladroite.
	spanish.therfcc.org /cube-impossible-554240.html (84 words)

	Blogger: Email Post to a Friend (Site not responding. Last check: 2007-09-20)
		Many Christians, as well as atheists, claim that it is impossible to prove a universal negative.
		Surely he would have known that it would have been better for those humans to never have been born (in fact, the Bible says this very thing), and surely this all-compassionate deity would have foregone the creation of a universe destined to imperfection in which many of the humans were doomed to eternal suffering.
		The existence of Yahweh is as impossible as the existence of cubic spheres or invisible pink unicorns.
	www.blogger.com /email-post.g?blogID=3429934&postID=90286350 (2135 words)

	Question Corner -- The Three Classical Impossible Constructions of Geometry
		The reason the three classical constructions are impossible is that they are asking you to be able to construct points whose coordinates are not numbers of this type.
		Doubling a cube is impossible because if you start with a cube of side length 1, you would need to cunstruct a cube whose side length is the cubed root of 2.
		Trisecting an angle is impossible because if you start with an angle of 60 degrees (which is easily constructible), you would then need to be able to construct an angle of 20 degrees.
	www.math.toronto.edu /mathnet/questionCorner/impossconstruct.html (909 words)

	We Ain't Cool (Site not responding. Last check: 2007-09-20)
		All of the cube shaped rooms are really just one room used over and over, but colored lighting makes it appear different.
		Cube has its share of problems, but is very impressive for having next to NO budget to work with.
		The first Cube was fair and there was a solution to the puzzle.
	www.weaintcool.com /Reviews/cubes.html (2269 words)

	There are really impossible things
		However, if you think that the only impossible things are trivial and those that depend on some kind of math trickery, think twice.
		There are a few known yet from antiquity that were attempted by dozens (and probably more) for thousands years until their impossibility has been revealed in recent times.
		Constructing a triangle from its angle bisectors is in general impossible
	www.cut-the-knot.org /impossible/index.shtml (293 words)

	halasz,hantos,faa
		A three-dimensional turning cube worked like a brush if one directed it and the effect of this rather special brush was a space construction (see ).
		The Impossible Cube made from strips of wood, was originally created by Escher so that the perspective would suggest directly opposite spatial relations one after the other.
		Now in each of the upper left, upper right, lower left, and lower right picture fields a small cube presenting the different spatial relations of the cube could be seen, and at the same time as a copy a large cube in the middle (see ).
	clcwebjournal.lib.purdue.edu /clcweb01-3/halasz&hantos&faa01.html (4728 words)

	Impossible objects - history (Site not responding. Last check: 2007-09-20)
		Probably the first intentionally painted impossible object was the gallows in Pieter Breughels canvas The magpie on the gallows of 1568 (Hessisches Landesmuseum Darmstadt, left a detail).
		Also interesting is the self-referring development that the discovery (invention?) of the impossible objects made: Oscar Reutersvärd already drawed them when he was a pupil, but actually was aware of his discovery after the publication of the Penroses' article.
		Escher in turn was inspired by the Penroses' article and invented the impossible cube, developed the Penroses' ideas (the impossible tribar and the endless stairway) further and applied them in numerous fantastic pictures.
	haegar.fh-swf.de /spielwiese/unmoeglicheObjekte/english/seite2.html (221 words)

	Maurits Cornelius Escher (Site not responding. Last check: 2007-09-20)
		A number of Escher's tilings have been used by crystallographers to illustrate the various ways in which the lattices in crystals arrange themselves.
		Escher became interested in "impossible" objects, those that are impossible in three dimensions, but can be created in two dimensions to make an illusion in three dimensions.
		The cube displayed on the stamp below is used in both Man with Cuboid and Belvedere, from 1958.
	sio.midco.net /danstopicalstamps/escher.htm (169 words)

	The Soma Cube (Site not responding. Last check: 2007-09-20)
		The SOMA cube was invented by Piet Hein, a Danish poet, dreamer, mathematician and genius; way back in 1936.
		Sadly, the disco-erazoic Soma Cube was smothered away into extinction by another puzzle during the pre-rappazoic period.
		In the meantime, you can educate yourself on the SOMA cube by visiting Thorleif's SOMA Page, maintained by my good friend Thorleif Bundgaard, who co-wrote the solving program with me. You can also download the SOMA-solving program (in .BAS ~or~ .EXE format) from there, along with instuctions on how to run the program.
	www.geocities.com /abcmcfarren/soma/soma.htm (826 words)

	The Impossible Cube (Site not responding. Last check: 2007-09-20)
		Put the pieces on a table so that three of the cubes of each are flat on the table's surface.
		Looking from above they should look like the letter v, arrange them so the the opening of the v's are facing each other, now bring them together until they touch at the corners.
		I guess that is why they call it the "Almost Impossible Cube".
	www.fam-bundgaard.dk /SOMA/NEWS/N030724.HTM (244 words)

	Promo that was posted last night everyone read (Site not responding. Last check: 2007-09-20)
		There is no right answer that everyone will agree on no it would be impossible like that rubrics cube or is it impossible.
		Some have said that the cube is impossible others have mastered it.
		Would you look at that, the glass is full the rubrics cube is solved, and the puzzle is finished with every piece in place.
	users4.cgiforme.com /swf3k/messages/401.html (1251 words)

	Time Cube (Site not responding. Last check: 2007-09-20)
		Cube is the most perfect form of opposites.
		Cube has 6 sides - or no top and bottom.
		Cube, and a curse of evil if they ignore
	www.timecube.com (1198 words)

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