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Topic: Cartesian co ordinates

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	Bloomsbury.com - Research centre
		In one dimension (in other words, on a line), Cartesian co-ordinates are defined by choosing a point known as the origin (with co-ordinate 0), and specifying a distance measure (how far away the point with co-ordinate 1 is from the origin).
		The points on the line now all have uniquely defined real number values; for example, if the point 1 is 1cm away from the origin, the point -243 is 243cm away from the origin in the opposite direction.
		A second line, the ordinate, is drawn through the origin at right-angles to the first line, and its co-ordinate system is defined in terms of that on the abscissa.
	www.bloomsbury.com /ARC/detail.asp?EntryID=101925&bid=2 (388 words)

	Map Co-ordinates
		However, it is often difficult to work with latitude and longitude on a flat map, particularly if we are interested in measuring geometric properties of features on the map such as distances, directions or areas.
		It is much easier to work with a Cartesian co-ordinate system on the map.
		However, it is much more common to base the Cartesian co-ordinate system on a particular map projection.
	www.fes.uwaterloo.ca /crs/geog165/mapcoords.htm (2367 words)

	Z-Matrix Manipulation (Site not responding. Last check: 2007-10-30)
		All cartesian co-ordinates are treated as fixed unless specified as variables, in the same manner as internal co-ordinates.
		The z_gen command allows a z-matrix to be constructed given cartesian co-ordinates and a specification of the atom indices from which the bond length, angle, and torsion definitions are derived.
		This command is generally used when an input cartesian definition is to be used as the starting point for the manual addition of atoms using internal coordinates.
	www.cse.clrc.ac.uk /qcg/chemshell/manual-3.0/zmatrix.html (2008 words)

	Ordnance Survey Ireland :: Geodetic services :: Overview :: Cartesian Co-ordinates
		It is important to realise that the centre of a Cartesian reference system for an adopted ellipsoid may not be the 'true' or adopted centre of mass of the earth - the latter is often used for global reference systems (as used by the Global Positioning System, GPS).
		This issue is not dealt with here, except to state that it is necessary to move from the ellipsoidal system to the local cartesian reference system before applying some translations in X, Y and Z, and possibly scale change and rotations around these axes as well, to move from the local system to global.
		The cartesian reference system is particularly useful as calculations are simpler to perform (no knowledge of spherical geometry being required).
	www.osi.ie /gps/overview/cartesian.asp (311 words)

	Radar display apparatus - Patent 4443797
		Thus, the Cartesian co-ordinates of each conversion is compared with the conversion in the previous range scan not only at the same range but also at the range increments on either side thereof.
		To achieve this, the azimuth angle of the aerial of the radar transmitter and receiver 10 is digitised by an azimuth digitiser 19 which produces azimuth pulses corresponding to unit changes in azimuth angle of the radar aerial.
		These Cartesian co-ordinates are fed, via the address bus 18, to the main memory 17 to address the respective locations in the three memory planes of the memory 17 for the read/modify/write sequence of the control unit 16.
	www.freepatentsonline.com /4443797.html (6740 words)

	Visualisation
		The diagonalisation of the mass-weighted Cartesian force constant matrix evaluated at a stationary point on the potential energy surface should yield six zero eigenvalues for translational and rotational motions and 3N-6 non-zero eigenvalues for vibrational modes.
		The small non-zero translational and rotational frequencies arising from force-constants that are computed directly in Cartesian co-ordinates are eliminated by means of a projection method which preserves only the internal co-ordinates contribution to the force constants.
		This symbol separates the co-ordinates and the Cartesian force constants that are subsequently appended to deck.
	www.bath.ac.uk /~chsihw/grace/camvib.html (653 words)

	Rene Decartes
		Cartesian co-ordinates are a system whereby the position of a point on a graph or map is gives by its distances from two lines.
		In two dimensional Cartesian co-ordinates, the lines, or axes, are named x and y.
		Whereas in three dimensional Cartesian co-ordinates the axes are name x, y, and z.
	web.ukonline.co.uk /mathematians.history/Descarte.htm (480 words)

	Relativity: Chpt. 24
		These two numbers are then the " Cartesian co-ordinates " of this corner with reference to the " Cartesian co-ordinate system" which is determined by the arrangement of little rods.
		The method of Cartesian coordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies.
		The surface is not a Euclidean continuum with respect to the rods, and we cannot define Cartesian co-ordinates in the surface.
	www.beyondweird.com /einstein/contents/ch24.htm (808 words)

	AutoCAD 2000i Tutorial - Using Co-ordinates
		Despite the fancy title (named after the French philosopher and mathematician René Descartes 1596-1650), the Cartesian co-ordinate system is the standard co-ordinate system.
		The main difference is that polar co-ordinates use one distance and one angle to describe the position of a point rather than the two distances in the Cartesian system.
		The distinction is quite simple, absolute co-ordinates relate to the X and Y axes and the origin of the current co-ordinate system, whilst relative co-ordinates relate to the current pick point.
	www.cadtutor.net /acad/acad2ki/coords/coords.html (1045 words)

	Rene Descartes - Famous mathematicians pictures, posters, gifts items, note cards, greeting cards, and prints
		Descartes' portrait is quadrisected by the axes of his great advance in analytical geometry: what has come to be known as the Cartesian plane.
		Descartes saw that a point in a plane could be completely determined if its distances (conventionally 'x' and 'y') were given from two fixed lines drawn at right angles in the plane, with the now-familiar convention of interpreting positive and negative values.
		Conventionally, such co-ordinates are referred to as "Cartesian co-ordinates".
	www.mathematicianspictures.com /Mathematicians/Descartes.htm (255 words)

	Gaussian Integrals
		ANGSTROM means that the input Cartesian co-ordinates will be assumed to be in Angstrom, and would be converted to atomic units by division by 0.529177.
		X,Y,Z are the Cartesian co-ordinates of the given centre, in the appropriate units.
		TEXT should be set to the character C. X,Y,Z are the Cartesian co-ordinates of the centre, and these fields may be set as valid floating point numbers, or as previously defind symbols.
	tc5.chem.uu.nl /ATMOL/integral.html (6885 words)

	Tutorial09
		(b) Show that the conversion formula for a triple integral from cartesian to spherical co-ordinates over a region S is given by:
		In evaluating this integral, first transform the cartesian co-ordinates to cylindrical polar co-ordinates.
		In evaluating this integral, first transform the cartesian co-ordinates to spherical polar co-ordinates.
	www.ens.gu.edu.au /albertg/2311aes/Tutorial11.html (360 words)

	Resources for Materials - Geometry - Polar co-ordinates - mathcentre
		The (x, y) co-ordinates of a point in the plane are called its Cartesian co-ordinates.
		But there is another way to specify the position of a point, and that is to use polar co-ordinates (r, theta).
		In this unit we explain how to convert from Cartesian co-ordinates to polar co-ordinates, and back again.
	www.mathcentre.ac.uk /students.php/materials/geometry/polar/resources (176 words)

	Roboforth II V10 manual
		Cartesian co-ordinates can be recorded in different ways: one is by using the defining word POINT e.g.
		In Cartesian mode all co-ordinates learned into a route are the Cartesian co-ordinates.
		Another way of using Cartesian commands is to position the robot, but then to create a PLACE name which will always contain joint co-ordinates even though the system is in Cartesian mode.
	www.strobotics.com /manuals/manual10.htm (18796 words)

	9. The GEOMETRY Directive (Site not responding. Last check: 2007-10-30)
		X, Y, Z are the Cartesian co-ordinates of the given centre, in the appropriate units.
		The sub-directive INTERNALS terminates cartesian input and allows the user to define the remaining atoms using standard z-matrix notation.
		If the second atom is also specified as cartesian, then the x and y coordinates must also be constants.
	www.cse.clrc.ac.uk /qcg/gamess-uk/manual-6.3/chap3/node10.html (1462 words)

	AdvancedBlocks
		The library has been extensively restructured to enhance the user friendliness and bring more of the options previously supported by Simelica into the library.
		Implements a conversion from cartesian co-ordinates to polar co-ordinates according to:
		Implements a conversion from cartesian co-ordinates to spherical co-ordinates according to:
	claytex.com /advancedblocks/AdvancedBlocks_Extras_Transformations.html (632 words)

	Module and Programme Catalogue
		(iii Explain what is meant by the derivative of a vector and perform simple calculations in Cartesian co-ordinates.
		(iv) Explain the relationship between Cartesian and cylindrical co-ordinates.
		(x) Know the definitions in Cartesian co-ordinates and be able to apply them in problems with simple geometry.
	www.leeds.ac.uk /modules/200203/ug/elec2710.htm (374 words)

	Matrices & Determinants (Site not responding. Last check: 2007-10-30)
		There are cases where even a square matrix cannot be so defined.
		An example of the use of matrices is the transformation of Cylinderical co-ordinates to cartesian co-ordinates in vector algebra..
		A transformation vector can be determined [A] such that the cartesian co-ordinate {V} cart
	www.roymech.co.uk /Useful_Tables/Form/Matrices.html (726 words)

	Lines of Intersection of planes in Cartesian co-ordinates. (Site not responding. Last check: 2007-10-30)
		Lines of Intersection of planes in Cartesian co-ordinates.
		Im at a loss as how to specify an equation for it.
		Re: Lines of Intersection of planes in Cartesian co-ordinates.
	www.mathguide.com /bbs/Messages2001/652.html (197 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		The theory of vectors is associated very closely with co-ordinate geometry so we shall start by introducing the co-ordinate system.
		We use a rectangular Cartesian co-ordinate system with axes
		The position of any point, P say, is given by co-ordinates (x, y, z) or (x
	www.efm.leeds.ac.uk /CIVE/CIVE2599/Notes/coordinates.html (104 words)

	Latest layout files including Cartesian co-ordinates (Site not responding. Last check: 2007-10-30)
		comma separator in address block), and Cartesian >co-ordinates of boxes (using top left as row 1, column 1).
		I was able to add the XPath addresses and the Cartesian co-ordinates.
		Adding the mixed content formatting has proved not at all easy, so I'm abandoning it for now, leaving it to the implementer to interpret mixed content from a visual example than from a formal specification for now.
	www.oasis-open.org /archives/ubl-hisc/200507/msg00009.html (228 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		The Cartesian co-ordinates (x, y, z) of a point on the unit-sphere follow from (2).
		EMBED Equation.3 (2) Thus the two pole vertices have the Cartesian co-ordinates (0, 0, 1) and (0, 0, -1), respectively.
		The geographical co-ordinates ( EMBED Equation.3 , EMBED Equation.3 ) of a point on the unit-sphere with the Cartesian co-ordinates (x, y, z) follow from (3) which may be derived from (2).
	www.wmo.ch /web/www/DPS/Icosah.doc (1318 words)

	mathsb
		d) significance of the constants A, B and C n the graphs of y - A sin (Bx + C) and y = A cos (Bx + C) e) applications of periodic functions
		where f(x) and g(x) are simple polynomial functions, simple exponential functions, sin x or cos x
		c) applications of the derivatives of sin x and cos x in life-related situations
	www.somerset.qld.edu.au /mathematics/mathsb.htm (1294 words)

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