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Topic: Three dimensional

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Hamel dimension

The Fifth Dimension

Super Dimension Fortress Macross

Hausdorff dimension

dimension of a vector space

The 5th Dimension

Why 10 dimensions

Krull dimension

Dungeon Dimensions

Lebesgue covering dimension

dimension of an algebraic variety

Dimension theorem for vector spaces

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	Three-Dimensional Chess
		In that case, it would make sense for the fl pieces to be arranged three rows deep on the top level instead of the bottom level, and for the kings and queens of both sides to face each other on the same file.
		Unfortunately, the three sides are in a relationship such that one is, in effect, before, and the other is after, the third player, so the array is not symmetric with only two players.
		Also, the top and bottom three levels are small rectangles; the green area simply shows where these rectangles stand in relation to the central 5 x 5 square of the five middle levels, so that alignment is unambiguous.
	www.hypermaths.org /quadibloc/chess/ch05.htm (1746 words)

	3-D - Wikipedia, the free encyclopedia
		Look up Three dimensional on Wiktionary, the free dictionary.
		Three dimensional, 3-D or 3D may refer to:
		Stereoscopy, recording 3 dimensional visual information or creating the illusion of depth in an image
	en.wikipedia.org /wiki/3D (132 words)

	The Game Of Three Dimensional Eight Level Chess
		In the Three Coordinate Algebraic System, the notation of a point is accomplished by naming the three common planes to the point.
		The three common planes are Level, Section and Degree; there are 8 of each, and they should always be named in that order (L, S, D).
		The three lines on the board in the diagram are the a8 column, the 3d file, and the 76 rank.
	www.hixoxih.com /games/chess/3D8L.htm (3544 words)

	Three-Dimensional Cursor
		Here the cursor position defines three intersecting lines, each line parallel to one of the principle axes of the volume (see Figure 1).
		This cursor defines the same three lines as in the three-dimensional overlay cursor, except that, instead of drawing the projected lines over the rendered volume, they are effectively merged into the data.
		For a maximum voxel algorithm each point along the three lines is drawn or not drawn according to whether the point is considered to be in front of or behind an obscuring feature, using the same depth estimation algorithm used by the two-dimensional active cursor.
	www.atnf.csiro.au /pasa/14_1/gooch/paper/node3.html (569 words)

	Viewing Four-dimensional Objects in Three Dimensions
		The sphere explains to the square the existence of higher dimensional objects like itself, and ways in which the square can understand the form of such objects.
		This method of viewing higher dimensional objects as well as others is one way people can understand the shape of higher dimensional space.
		A second way to view three dimensional polytopes in two dimensions is by means of a projection.
	www.geom.uiuc.edu /docs/forum/polytope (977 words)

	Dimension article - Dimension Latin degrees freedom measurements shape Physical dimensions - What-Means.com (Site not responding. Last check: 2007-10-21)
		For example, the space in which we live appears to be 3-dimensional.
		We can move up-or-down, north-or-south, or east-or-west, and movement in any other direction can be expressed in terms of just these three.
		Moving down is the same as moving up a negative amount.
	www.what-means.com /encyclopedia/Three-dimensional (596 words)

	Three-dimensional chess - Wikipedia, the free encyclopedia
		This variant is played on three standard 8×8 boards, stacked vertically.
		The movements of various pieces have been modified to allow them to move across boards (for example the Cannon must move three spaces in one direction, two in a perpendicular direction and one in the remaining perpendicular).
		A variant possibly similar to Star Trek 's Tri-Dimensional Chess is seen in Legend of Galactic Heroes, a Japanese science fiction novel.
	en.wikipedia.org /wiki/Three-dimensional_chess (737 words)

	Three Dimensional Hyperbolic Positioning and Synthesizable VHDL Code / GPS satellite (Site not responding. Last check: 2007-10-21)
		This paper presents the detailed derivation of an algorithm for obtaining an exact solution for the three dimensional location of a mobile given the locations of four fixed stations (like a GPS satellite or a base station in a cell) and the signal time of arrival (TOA) from the mobile to each station.
		Some methods calculate the two dimensional position and others the three dimensional position depending on the degree of simplicity desired.
		In this paper, a more detailed derivation of a set of equations needed to locate the three dimensional position of a mobile is presented.
	ralph.bucher.home.att.net /project.html (1293 words)

	Explicit Links to Three Dimensional Shape
		People also appear to have difficulty reasoning about motion in three independent dimensions, so limiting a robot reasoning system to two dimensions for actual motion planning may be an acceptable restriction if human-like performance is the goal.
		These two dimensions might be in either a cartesian or polar co-ordinate system, since simultaneous turning and linear motion in the case of screw operation is not a difficult reasoning problem for people.
		In three dimensions, there are six types of possible contact: plane-plane, plane-edge, plane-vertex, edge-edge, edge-vertex and vertex-vertex.
	www.cl.cam.ac.uk /~afb21/publications/masters/node66.html (276 words)

	An Unshellable Triangulation (Site not responding. Last check: 2007-10-21)
		The higher dimensional analog of a triangle is a simplex.
		In the plane a triangulation can always be built by starting with one triangle and then adding one triangle at a time so that at every step one has a set of triangles whose union forms a polygon that can be continuously deformed into a square (i.e., it's homeomorphic to a square).
		Unfortunately, to appreciate this example interactive manipulation to show the three dimensional structure is almost essential.
	www.math.utah.edu /~alfeld/Rudin.html (536 words)

	three dimensional puzzles - Find, Compare, and Buy at Shopping.com
		This Three Dimensional Plastic Dinner Meal Puzzle is an excellent teaching tool for table etiquet......
		This Three Dimensional Plastic Meal Puzzle is called lunch and makes an excellent teaching tool f...
		With just eight pieces, this three dimensional cube consisting of six different colors that magically changes to a 2 dimensional flat puzzle with a rainbow image using the same 8......
	www.shopping.com /xGS-three_dimensional_puzzles (879 words)

	The Geometer's Sketchpad® - : Hypercube
		This creates a vector—an arrow representing distance and length—by which to move point P. The image of point P as it moves along this vector—P's locus—is a one-dimensional object: a line segment.
		So we can create a one-dimensional object out of a zero-dimensional object by translating it along some vector.
		But there's a problem: While the image of P translated by three vectors in turn might now look like a cube, it can't be a cube: the screen is flat (two-dimensional), and the picture of the cube lies within the plane of the screen.
	www.keypress.com /sketchpad/javasketchpad/gallery/pages/hypercube.php (640 words)

	Usefulness of three dimensional ultrasonography for invisible fundus -- ENDO et al. 84 (9): 1075 -- British Journal of ...
		Usefulness of three dimensional ultrasonography for invisible fundus -- ENDO et al.
		Two dimensional ultrasonography has traditionally been used to examine retinal or vitreous diseases with invisible fundus.
		This case was successfully examined by three dimensional ultrasonography.
	www.bjophthalmol.com /cgi/content/full/84/9/1075g (551 words)

	Presenting the new three-dimensional periodic table that is the future of Chemistry Education (Site not responding. Last check: 2007-10-21)
		But the elements can be traced with a finger by their electron numbers in sequence without changing direction or leaving the surface when the sheet is formed into three dimensions.
		Including these three main improvements, the patented Alexander Arrangement of the Elements presents to the student a learning aid in a natural, logical form of unprecedented clarity.
		Now that the illustrations have served their purpose we remove the part with three round segments to make a filler that will help the sandd-block section assume a rounder shape.
	periodictable.com /pages/3AAE3D.html (1178 words)

	Three Dimensional LLC - Business Solutions with Added Perspective
		Department “A” looked at their processing and determined that by eliminating three steps they could reduce their costs by $110,000 (a 12% reduction).
		However, the elimination of the three steps in department “A” had unforeseen, detrimental effects on department “B” - the Rule of Unintended Consequences.
		The removal of these steps in department “A” eliminated the ability of department “B” to maintain their quality control program, which resulted in a 9% increase in the number of policies rated incorrectly.
	www.3-dllc.com /white_papers.html (706 words)

	Three Dimensional N*N-Queens Problems
		QP solution replicated infinitely many times in three dimensions, it scatters points very uniformly in space at a density of 1/N. Other variants on the 2DNQP have been studied [3].
		If we name the three visible faces S, S' and S", then either they are all linear Latin squares or none of them are.
		Shapiro proved the remarkable result that there is a Latin square over a set of generators iff there is a linear Latin square over the generators.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Recn/Queens3D (1527 words)

	Combinatorial Tiling Theory (Site not responding. Last check: 2007-10-21)
		Together with Klaus Westphal, a further algorithm was developed that solves the realization problem for all three classical 2-dimensional geometries (Westphal 1991 and Huson 1996).
		In three dimensions, no such simple invariant is known.
		In particular, we have clarified the relationship between the geometry of periodic tilings, the topology of orbifolds, and the combinatorics of parameterized Coxeter matrices or Delaney symbols.
	www.mathematik.uni-bielefeld.de /~huson/approach.html (3565 words)

	Three Dimensional Structures (Site not responding. Last check: 2007-10-21)
		It is best to start by building real models of some of the molecules with a model set.
		After some work with models, it is easier to see them in three dimensions on paper.
		There are pictures of three-dimensional models of many molecules in the text, but, even after working with a model set, is it often still difficult to actually visualize these molecules in three dimensions.
	www.du.edu /~jhornbac/organic/struct3d.html (408 words)

	Riding the Meridian -- Three-Dimensional Dementia 1 by Carolyn Guertin
		Forgetting is a part of living in the text, and short term memory is constantly being bombarded by cues, clues and flashbacks in 800 screens of text and images.
		Califia is a genealogical "treasure map" that reconnects a forgotten web of stories and legends of three prospecting California families over five generations.
		A complex user interface divides the text into four journeyings, each of which is a doorway into the narrative: they are South (The Comets in the Yard), East (Wind, Sand and Stars), North (The Night of the Bear) and West (The Journey Out).
	www.heelstone.com /meridian/guertin/3DD1.htm (632 words)

	SYMMETRY OF THREE-DIMENSIONAL QUASICRYSTALS (Site not responding. Last check: 2007-10-21)
		Projection of a regular lattice of higher dimension into the real physical space of lower dimension is a very useful method to construct a model structure of general lattices unifying usual lattices and quasilattices; the well-known examples are one-dimensional quasilattice as a projection from two-dimension, 2D-PT from five-dimension and three-dimensional quasilattice from six-dimension.
		The radii along three kinds of symmetry axes and to the edges are tabulated in Table 8.
		As a three- dimensional point configuration, they are regardes as 22 vertices of a 30-hedron with bottleneck, among whose 30 faces 10 are equilateral triangles, the other 10 are another kind of equilateral triangles and the last 10 are trapezia.
	www.mi.sanu.ac.yu /vismath/ogawa/3da.htm (2119 words)

	Three-Dimensional Sketching
		The modeling space is characterized by a noun-verb syntax direct -manipulation interface, using direct mouse control of a crosshair in three dimensions and objects with click-selectable handles to achieve facile editing in three dimensions.
		The basic requirements of the create, select, and edit operations don't really change when we jump to three dimensions, and the kinds of visual status feedback provided by the Macintosh drawing tools would be just as invaluable in a three-dimensional model space as they are on a two-dimensional screen.
		There is a further difficulty in defining a three dimensional sketch interface by metaphor.
	www.designlaboratory.com /faculty/matthews.kevin/research/mp3.02b.html (10470 words)

	Three Dimensional Bowtie Blocks
		Materials required are five (5) equal sized squares of fabric -- two squares of background color and three squares for contrast.
		Leave your machine needle down while you adjust fabric of center folded square so that its remaining raw edges lie flat and unwrinkled.
		You now have a Three Dimensional Bow Tie block (Figure 8).
	www.quilterbydesign.com /lessons/bowtie.html (424 words)

	Three-Dimensional Electron Optics Model for Traveling-Wave Tubes
		Because these two-dimensional codes cannot adequately simulate a number of important effects, the simulation code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm) was used at Glenn to develop a three-dimensional electron optics model (refs.
		First, a PPM stack was modeled in three dimensions.
		Then, the fields obtained using the magnetostatic solver were loaded into a particle-in-cell solver where the fully three-dimensional behavior of the beam was simulated in the magnetic focusing field.
	www.lerc.nasa.gov /WWW/RT1999/5000/5620kory.html (511 words)

	Three-dimensional structure of the human transglutaminase 3 enzyme: binding of calcium ions changes structure for ... (Site not responding. Last check: 2007-10-21)
		In (C), the gray color represents the zymogen and the magenta color is the activated form.
		The three changed loop regions of the activated form, Ile223–Val231, Leu319–Ser325 and Tyr439–Asp446, are shown in green.
		three Ca ions that are required for enzyme activity.
	embojournal.npgjournals.com /cgi/content/full/21/9/2055 (6544 words)

	BioMed Central \| Full text \| Visualising very large phylogenetic trees in three dimensional hyperbolic space
		We introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format.
		These tools lay out trees in a two dimensional Euclidean space and are useful for visualising trees of up to a few hundred nodes.
		Some software tools, like Hypertree [6], have increased the number of visualisable nodes using 2D hyperbolic space to provide a "focus+context" view, where a subset of the data can be viewed at higher resolution with the remaining contextual data still in view (see the Deep Green project for an example with plant phylogenies [7]).
	www.biomedcentral.com /1471-2105/5/48 (1609 words)

	MICROSCOPY UK - MICSCAPE ARTICLE: Three dimensional photography through the Microscope
		How to make a stereoscope from a binocular and how to make three dimensional pictures from live organisms.
		I could take instant three dimensional pictures with it.
		When the filters are at the right place you can see the image three dimensional.
	www.microscopy-uk.org.uk /mag/art97b/wim2.html (957 words)

	Weddings
		The Wedding Ring Box is four inches long, stands one and three quarter inches high and is two inches deep.
		Other Studio boxes can be personalized in the same manner, or we can apply monograms or art features of your choice for use as gifts for members of the wedding party.
		Please allow three to four days for laser impression work.
	sattvagallery.com /weddingring.html (270 words)

	3D Ultrasound Resource - Research
		They have recently released a version of their 3D ultrasound aquisition software Stradx that runs under Irix 6.2 on SGI machines using a standard 2D ultrasound machine and an electromagnetic position/orientation sensor (Ascension Technology Corp. or Polhemus devices).
		The SOLUS-3D project is focused on the development of visualisation and measurement techniques based on three dimensional diagnostic ultrasound.
		The objectives of the Stradivarius Project are to establish a working system for the acquisition, processing and visualisation of three dimensional ultrasound data in a clinical environment.
	www.cs.uwa.edu.au /~bernard/us3d/research.html (1405 words)

	Three Dimensional Bubble Sort
		Depending on it's red content, it experiences a force moving it up or down the screen, and depending on the amount of each of the other two colours, it experiences forces moving it diagonally left and right.
		It's final resting position is the vector sum of these three forces, in relation to all the other pixels on the screen.
		This sorting algorithm can be taken to even higher dimensions, and can be applied to any combination of properties, not just the colours of pixels.
	www.magma.ca /~gtaylor/3dBubbleSort.htm (891 words)

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