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Topic: Two 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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	SparkNotes: Geometric Measurements: Measuring Two-Dimensional Figures
		Regions in a plane have a number of interesting properties that one-dimensional figures don't.
		Two such properties, and very important ones at that, are perimeter and area.
		The area of a region in a plane is the rough equivalent of the length of a one-dimensional object: it is the most important and applicable property of figures in that dimension, and is the main trait through which regions in a plane can be compared.
	www.sparknotes.com /math/geometry2/measurements/summary.html (376 words)

	Crystallisation of Two-Dimensional Cellular Automata
		First, various CA evolution patterns are analysed by the entropy function, and it is suggested that there are two types of CAs with static or chaotic evolution.
		These are the two extreme cases, and in the case of general rules, the mapping may or may not change cell states depending on the neighbour state.
		Equation (4) is the extension of this condition to two dimensions and ensures the expanding dynamics of 2-dimensional CAs.
	journal-ci.csse.monash.edu.au /ci_louise/vol06/suzudo/suzudo.html (2383 words)

	Crystallisation of Two-Dimensional Cellular Automata
		First, various CA evolution patterns are analysed by the entropy function, and it is suggested that there are two types of CAs with static or chaotic evolution.
		These are the two extreme cases, and in the case of general rules, the mapping may or may not change cell states depending on the neighbour state.
		Equation (4) is the extension of this condition to two dimensions and ensures the expanding dynamics of 2-dimensional CAs.
	www.complexity.org.au /ci/vol06/suzudo/suzudo.html (2383 words)

	Two-dimensional
		There are two different ways to compute the wavelet transform of two-dimensional data.
		The two dimensional basis is given by the collection of functions
		IFWT2 -- two dimensional inverse wavelet transform A = ifwt2ns(w, h, g) Input: w two dimensional wavelet coefficients h,g filter coefficients for the scaling function and wavelet Output: A inverse transform of w See also FWT2, IFWT2TNS, FWT2TNS, IFWT1, IFWT1NS.
	www.math.rutgers.edu /~ojanen/wavekit/node13.html (372 words)

	Interactive Chaos: What is a Multi-Dimensional Map?
		Since you need two different expressions to specify the initial conditions, it should be no surprise to you that in a two-dimensional map, you need two different rules for how the points will transform.
		In other words, even though the two equations of the map form a set together, they are completely independent of each other in how they act on the coordinates of a point.
		The two equations of the map are coupled together because in the second equation, both coordinates appear on the right-hand side.
	order.ph.utexas.edu /standardmap/twodimensional.html (971 words)

	Two-Dimensional Semantics
		For example, one might suppose that when two singular terms are cognitively equivalent (so that 'a=b' is trivial or at least knowable a priori, for example), then their extension will coincide in all possible worlds, so that they will have the same intension.
		And one might suppose that when two such terms are cognitively distinct (so that 'a=b' is knowable only empirically, for example), then their extensions will differ in some possible world, so that they will have different intensions.
		The framework does have two semantic values: the proposition expressed by an sentence, which is something like the familiar proposition that is true in all worlds where Whitworth invented the zip, and the content of the sentence, which behaves as characterized above.
	consc.net /papers/twodim.html (14816 words)

	Two-Dimensional Cellular Automata (1985)
		The two entries for reflectional symmetries of the hexagonal lattice refer to reflections across a cell and across a boundary, respectively.
		Empirical studies strongly suggest that the qualitative properties of one-dimensional cellular automata are largely independent of such features of their construction as the number of possible values for each site, and the size of the neighborhood.
		A new feature in two dimensions is the generation of patterns with dendritic boundaries, much as observed in many natural systems.
	www.stephenwolfram.com /publications/articles/ca/85-two/2/text.html (1366 words)

	13.1 Two dimensional arrays
		Such a structure is known as a two dimensional array and consists of an array whose component elements are themselves arrays.
		However, as with one dimensional arrays, this merely states that it is a two dimensional array; it does not actually construct the array.
		As with one dimensional arrays the first element of each dimension of the array is in the zeroeth index location, so this pattern of indexes will ensure that each element is visited in turn.
	www.scism.sbu.ac.uk /jfl/Chapter13/chap13p1.html (583 words)

	A Two Dimensional Derivative of Boundary Representation
		The second approach which I took to two dimensional qualitative geometry was developed from boundary representation methods rather than from constructive solid geometry methods.
		The generalised cones method requires that a method of representing two dimensional shape be used to describe the cross section for ``sweeping'' operations, but a boundary representation must describe the two dimensional shape of every face in the three dimensional object.
		This has the advantage that individual features are separately described in local two dimensional contexts for the whole object, whereas for CSG, features in planes other than the cross section must be inferred from the sweeping function.
	www.cl.cam.ac.uk /~afb21/publications/masters/node45.html (371 words)

	Two-dimensional auto compensated multi-axis tolerance adaptive system - Patent 6736483
		wherein said carrier unit has a rear sidewall, two lugs protruded from top and bottom sides of said rear sidewall and defining a respective pivot hole for pivoting to said rotating unit, and a serrated portion formed in said rear sidewall and meshed with said rotating unit.
		For example, the axle of the ink cartridge carrier and the axles of the media feed roller assembly may not perfectly be set in parallel, the axles may be biased due to an error of the related axle bearings or axle holes.
		The rotating unit 30 further comprises two pivot pins 36 axially aligned with the rotary driver 31 and respectively pivoted to the pivot holes 18 of the lugs 15 of the carrier unit 1.
	www.freepatentsonline.com /6736483.html (2296 words)

	The Physics Classroom
		The sum of these two vectors is not 30 000 kgm/s; this would only be the case if the two* momentum vectors had the same direction.
		Since the two momentum vectors are at right angles, their sum can be found using the Pythagorean theorem; the direction can be found using SOH CAH TOA (specifically, the tangent function).
		An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 250 000 Joules (200 000 J for the eastbound car plus 50 000 J for the northbound car).
	www.physicsclassroom.com /mmedia/momentum/2di.html (579 words)

	A Two-Dimensional Constraint Solver (cont.)
		Let p1 and p2 be two points and l1(n1, r1) and l2(n2, r2) be two lines, where ni is the unit normal of li, and ri is the signed distance from li to the origin.
		Again for angle constraints, the orientations of the two line segments are used to determine which region between the segments should be affected by the constraint.
		These two cases are identical to cases 2 and 3, respectively, since pairwise constraints exist between all three entities.
	www.cs.purdue.edu /homes/cmh/electrobook/our_solver2.html (1105 words)

	Solution Set - Two Dimensional Motion - Physics 104
		Because the two vectors lie along the same straight line, I have drawn the vector for -6 m below the vector for +8 m.
		Remember two vectors are equal if they have the same magnitude and direction even if they do not start at the same point.
		The object is subjected to two different influences, an initial velocity and a continuing acceleration due to gravity, and the object responds to each without altering its response to the other.
	www.wellesley.edu /Physics/phyllisflemingphysics/n104_s_2dimmotion.html (988 words)

	Dimension - Wikipedia, the free encyclopedia
		The corresponding space has therefore two dimensions, its dimension is two, and this space is said to be 2-dimensional (2D).
		The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that n+1-dimensional balls have n dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets.
		The Krull dimension of a commutative ring, named after Wolfgang Krull (1899 - 1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.
	en.wikipedia.org /wiki/Two-dimensional (1528 words)

	Two-dimensional fiber optic acceleration and vibration sensor - Patent 5837998
		This invention relates to a two-dimensional fiber optic acceleration and vibration sensor for measuring two perpendicular components of an acceleration, velocity, displacement and frequency spectrum of a moving object to which the sensor is attached, utilizing an optical lever and a dual-axis position photosensor.
		Then module 22 generates signals proportional to the measured accelerations a.sub.X and a.sub.Y. These two signals are integrated separately in module 23 and a new pair of signals proportional to the velocity V.sub.X and V.sub.Y of the moving object are generated.
		These two signals are further integrated in module 24 and a new pair of signals proportional to the object displacement X and Y are generated.
	www.freepatentsonline.com /5837998.html (3310 words)

	Lab 14: Two Dimensional Arrays
		This two-dimensional array may be viewed as a one-dimensional array having 40 elements where each element is an array of 14 values.
		We should use two loops--one to control the student (row) and one to control the lab (column).
		As with one-dimensional arrays, a two-dimensional array is automatically passed as a pass-by-reference parameter.
	www.mtsu.edu /~csci117/manual/lab14/lab14.html (1250 words)

	Two Dimensional Morphing using the Extended Gaussian Image
		The problem therefore becomes that of moving the weights of the EGI on the unit sphere to redistribute them such that the EGI of the source polyhedron becomes that of the target, while keeping the center of mass at the origin (so that all intermediate objects are closed themselves).
		This approach allows us to get around the problem of matching two objects of different connectivity by letting the inverse EGI function create faces of arbitrary shape, our program having specified only their size and normal direction by moving the weights on the three dimensional sphere.
		The same source and target triangles presented in the two previous examples can also be transformed into one another by a simply rotation, which the program has found by increasing the angle cost a little more.
	web.mit.edu /manoli/ecimorph/www/ecimorph.html (1721 words)

	NOVA \| The Elegant Universe \| Imagining Other Dimensions \| PBS
		The sphere, now the shortsighted one of the two, cannot comprehend this and does not accept the square's arguments—just as most of us "spheres" today do not accept the idea of extra dimensions.
		Instead of one added dimension we have two if we consider only the spheres' surfaces and three if we take into account the space within the sphere.
		It turns out that, before superstring theory existed, two mathematicians, Eugenio Calabi of the University of Pennsylvania and Shing-Tung Yau of Harvard University, described six-dimensional geometrical shapes that superstring theorists say fit the bill for the kind of structures their equations call for.
	www.pbs.org /wgbh/nova/elegant/dimensions.html (1174 words)

	Engine Block: Effectiveness of two dimensional opacity functions (Site not responding. Last check: 2007-09-17)
		While the method for one dimensional opacity function generation works passably with the dataset, the two dimensional opacity functions are very effective.
		The same boundary emphasis function used earlier for one dimensional opacity function generation is used again to generate the two dimension opacity function seen in Figure 6.7(b).
		Next, region two is removed from the opacity function, producing a rendering (Figure 6.7(f)) which shows only the boundary between the highest and lowest data values.
	www.cs.utah.edu /~gk/MS/html/node23.html (888 words)

	Two Dimensional Illusiuons
		Three dimensional effects were greeted as a sensational, almost magical illusion that made painting into a kind of magic window into a very believable world.
		The greatest leap forward in the representation of three dimensional space occurred in the 15th century, with the discovery of linear perspective.
		It is also possible to break all of these rules purposely in order to create three dimensional illusions that can fool the viewer and/or could never exist in an actual three dimensional model.
	char.txa.cornell.edu /language/element/form/formillu.htm (1380 words)

	9.1 Two Dimensional Arrays
		The two dimensional array as as argument must be declared in the function definition as a formal parameter.
		Recall, the two dimensional array is an array of rows.
		The difference is that now we use a two dimensional array for all float payroll data instead of several one dimensional arrays.
	www-ee.eng.hawaii.edu /Courses/EE150/Book/chap9/section2.1.1.html (1902 words)

	Two-dimensional Cuts
		Analogous to one-dimensional cuts, two-dimensional cut mean the condition of a pair of values being in a certain range, where the range is defined by a closed polygon in the x/y space.
		This is no longer done easily by hand, as in the case of one-dimensional cuts.
		As their one-dimensional counterparts, cuts are read from file either via the cut pull-down menu or with the
	www.iskp.uni-bonn.de /gruppen/edda/daq/yoda/node30.html (331 words)

	The Foundations of Two-Dimensional Semantics (Site not responding. Last check: 2007-09-17)
		When two tokens of the same expression type have different extensions, this reflects a difference in the context in which the tokens are embedded.
		We require this as the sentences S whose epistemic intensions we are defining are tokens, and it is possible for two sentence tokens of the same linguistic type to have different epistemic properties (for the reasons, see section 3.8).
		We can say that two possible individuals (at times) are twins if they are physical and phenomenal duplicates; we can say that two possible expression tokens are twins if they are produced by corresponding acts of twin speakers.
	consc.net /papers/foundations.html (21126 words)

	Motion in Two Dimensions
		In two dimensions, it is necessary to use vector notation to describe physical quantities with both magnitude and direction.
		In this chapter, we define displacement, velocity and acceleration as vectors in two dimensions.
		We also discuss the solution of projectile motion problems in two dimensions.
	theory.uwinnipeg.ca /physics/twodim/index.html (45 words)

	Two & Three Dimensional Systems
		This is a two-dimensional dynamic system in which two variables grow, but one grows at the expense of the other.
		There are two dimensions, x representing the sideways displacement of the column, and y the velocity of its movement.
		Shown next are two situations, differing in the magnitude of the mass.
	www.vanderbilt.edu /AnS/psychology/cogsci/chaos/workshop/2DS.html (1032 words)

	ArtLex's Tr-Tz page
		North Italian Painter, first quarter 14th century, Two Angels, fresco; (the one shown) 23 3/8 x 31 1/2 inches (59.4 x 80 cm); (the second) 23 1/2 x 31 1/2 inches (59.7 x 80 cm), Metropolitan Museum of Art, NY.
		That the two symmetrical chapels appear to have approximately the same vanishing point is an astonishing anticipation of the fifteenth-century perspective system.
		German, two 16th century woodcuts: first: the casting of type in a mold, and second: two men work the press, while behind them, another man sets the type.
	www.artlex.com /ArtLex/Tr.html (4738 words)

	2D computer graphics - Wikipedia, the free encyclopedia
		This technique is known as inverting color or color inversion, and is often used in graphical user interfaces for highlighting, rubber-band drawing, and other volatile painting—since re-painting the same shapes with the same color will restore the original pixel values.
		Layers that consist of complex geometric objects (such as text or polylines) may be broken down into simpler elements (characters or line segments, respectively), which are then painted as separate layers, in some order.
		The user interface within individual software applications is typically 2D in nature as well, due in part to the fact that most common input devices, such as the mouse, are constrained to two dimensions of movement.
	en.wikipedia.org /wiki/2D_computer_graphics (1517 words)

	Two-Dimensional Cellular Automata (1985)
		As mentioned in Section 1, four qualitative classes of behavior have been identified in the evolution of one-dimensional cellular automata from disordered initial states.
		A rough analog of this behavior is found in asymmetric one-dimensional cellular automata which generate symmetrical difference patterns.
		It appears that as the number of parameters or degrees of freedom in a cellular automaton rule increases, there is a higher probability for some degree of freedom to show chaotic behavior, leading to overall chaotic behavior.
	www.stephenwolfram.com /publications/articles/ca/85-two/4/text.html (1894 words)

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