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Topic: Cartesian coordinates


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  Cartesian coordinate system - Wikipedia, the free encyclopedia
Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry.
The modern Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane).
It may be interesting to note that some have indicated that the master artists of the Renaissance used a grid, in the form of a wire mesh, as a tool for breaking up the component parts of their subjects they painted--a trade secret.
en.wikipedia.org /wiki/Cartesian_coordinates   (1106 words)

  
 Coordinates (mathematics) - Wikipedia, the free encyclopedia
The coordinates of a point are the components of a tuple of numbers used to represent the location of the point in the plane or space.
The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles.
In terms of the Cartesian coordinate system, one usually picks O to be the origin (0,0) and L to be the positive x-axis (the right half of the x-axis).
en.wikipedia.org /wiki/Coordinates_(elementary_mathematics)   (1186 words)

  
 Cartesian coordinates
In coordinate geometry, components used to define the position of a point by its perpendicular distance from a set of two or more axes, or reference lines.
The Cartesian coordinate system can be extended to any finite number of dimensions (axes), and is used thus in theoretical mathematics.
Coordinates can be negative numbers, or a positive and a negative; for example (−4, −7), where the point would be to the left of and below zero on the axes.
www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0006650.html   (273 words)

  
 GLOSSARY - Cartesian Coordinates   (Site not responding. Last check: 2007-11-07)
Cartesian coordinates (named after Descartes) are used to specify a point on a 2 dimensional surface by the horizontal distance and the vertical distance of the point from the horizontal and vertical zero reference points.
Polar coordinates are used to specify a point on a 2 dimensional surface by its diagonal distance (radius) of the point from the horizontal and vertical zero reference points and the angle the diagonal would make with the horizontal (3 o'clock position).
Coordinate Conversion is the conversion from Cartesian coordinates to Polar coordinates or vice versa as discussed in POLAR AND CARTESIAN COORDINATES.
www.magma.ca /~masonjl/Glossary/glos3s6r.htm   (146 words)

  
 AllRefer.com - Cartesian coordinates (Mathematics) - Encyclopedia
Cartesian coordinates[kArtE´zhun] Pronunciation Key [for RenE Descartes], system for representing the relative positions of points in a plane or in space.
In a plane, the point P is specified by the pair of numbers (x,y) representing the distances of the point from two intersecting straight lines, referred to as the x-axis and the y-axis.
In oblique coordinates the axes are not perpendicular; the abscissa of P is measured along a parallel to the x-axis, and the ordinate is measured along a parallel to the y-axis, but neither of these parallels is perpendicular to the other coordinate axis as in rectangular coordinates.
reference.allrefer.com /encyclopedia/C/Cartes-coo.html   (279 words)

  
 Coordinates
Coordinates are sets of numbers that describe position-- position along a line, on a surface or in space.
Cartesian c oordinates (x,y) are not the only way of labeling a point P on a flat plane by a pair of numbers.
In three dimensional space, the cartesian labeling (x,y,z) is nicely symmetric, but sometimes it is convenient to follow the style of polar coordinates and label distance and and direction separately.
www-spof.gsfc.nasa.gov /stargaze/Scelcoor.htm   (966 words)

  
 Cartesian coordinates - a Whatis.com definition
Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional (3D) space.
Positions or coordinates are determined according to the east/west and north/south displacements from the origin.
Positions or coordinates are determined according to the east/west (x), north/south (y), and up/down (z) displacements from the origin.
whatis.techtarget.com /definition/0,,sid9_gci824296,00.html   (436 words)

  
 Cartesian coordinates on Encyclopedia.com   (Site not responding. Last check: 2007-11-07)
In a plane, the point P is specified by the pair of numbers (x,y) representing the distances of the point from two intersecting straight lines, referred to as the x -axis and the y -axis.
In oblique coordinates the axes are not perpendicular; the abscissa of P is measured along a parallel to the x -axis, and the ordinate is measured along a parallel to the y -axis, but neither of these parallels is perpendicular to the other coordinate axis as in rectangular coordinates.
Cartesian Data announces breakthrough in data storage technology for higher capacity, low cost mobile applications; new company's proprietary TMT technology offers alternative to conventional disk drive and FLASH...
www.encyclopedia.com /html/C/Cartes-coo.asp   (498 words)

  
 [No title]   (Site not responding. Last check: 2007-11-07)
The most common coordinate system used is the Cartesian coordinate system (named after Descartes).
In constructing your coordinate system, you must first choose a point to be the origin, then draw two axes, i.e.
The coordinates of the point marked with a cross are the x and y values at that point.
www.ucl.ac.uk /Mathematics/geomath/rev/graphnb/graph3.html   (236 words)

  
 Cartesian Coordinates   (Site not responding. Last check: 2007-11-07)
For accurate work, Cartesian (XYZ) coordinates are much to be preferred, since the use of latitude, longitude and height entails a number of possible uncertainties and ambiguities.
Notes: The coordinates are in a conventional geocentric right-handed Cartesian system, with the Z axis parallel to the mean rotation axis (North) and the X-axis aligned towards the intersection of the Greenwich meridian and the equator.
The antenna coordinates used by CAOBS for array pointing prior to October 1991 were all approximately 200m in error (mostly a uniform translation) owing to a misconception of references systems in the surveyors' report.
www.narrabri.atnf.csiro.au /observing/users_guide/html/node215.html   (542 words)

  
 [No title]
A system of coordinates for location a point on a plane by its distance from each of two perpendicular intersecting lines, or in space by the distance from each of three mutually perpendicular planes intersecting at a point.
The chromaticity coordinates of a stimulus are derived from its tristimulus values by taking the ratio of each of the tristimulus values to their sum.
The color space coordinates of a color space with a larger gamut are reduced to accommodate the smaller gamut of a destination color space.
home.wanadoo.nl /paulschils/01.02.html   (3332 words)

  
 Cartesian Coordinates
In Cartesian coordinate system, one deals with a group of mutually perpendicular axes (or planes).
For this reason, the Cartesian coordinate system is also called the rectangular coordinate system.
This is the traditional 3-D Cartesian coordinate system and will be used consistently throughout this website.
kwon3d.com /theory/crdsys/cart.html   (250 words)

  
 Polar Coordinates
The 2-D polar coordinate system involves the distance from the origin and an azimuth angle.
The polar coordinates are useful in describing the human body motion since the essence of the human body motion is the joint motions.
In some cases, one may use the Cartesian coordinates in the sense of the polar coordinates, as shown on
kwon3d.com /theory/crdsys/polar.html   (408 words)

  
 Polar coordinates
From a polar equation to a cartesian equation
Call (x,y) the cartesian coordinates of P. According to the previous definition, the cartesian coordinates of U are (cos t, sin t).
To convert the equation of K to a cartesian equation, we appeal on the properties of Polar equation of a conic section.
www.ping.be /~ping1339/polar.htm   (3425 words)

  
 Spherical Coordinates   (Site not responding. Last check: 2007-11-07)
In the last module we looked at cylindrical coordinates -- a system of coordinates that is very useful when the important things about a three-dimensional point are its distance from the z-axis and its angle from the positive xz-plane.
The third coordinate -- theta -- is identical to the coordinate theta used in cylindrical coordinates.
This system of coordinates is very similar to the system -- longitude and latitude -- of coordinates used to describe points on the earth's surface.
www.math.montana.edu /frankw/ccp/multiworld/multipleIVP/spherical/body.htm   (1849 words)

  
 Coordinate Systems   (Site not responding. Last check: 2007-11-07)
The most common coordinate system for representing positions in space is one based on three perpendicular spatial axes generally designated x, y, and z.
Any point P may be represented by three signed numbers, usually written (x, y, z) where the coordinate is the perpendicular distance from the plane formed by the other two axes.
Although the entire coordinate system can be rotated, the relationship between the axes is fixed in what is called a right-handed coordinate system.
hyperphysics.phy-astr.gsu.edu /hbase/coord.html   (117 words)

  
 Locating Points Using Cartesian Coordinates   (Site not responding. Last check: 2007-11-07)
To use the coordinate system in locating places on the map.
The students will give the coordinates of points on the plane.
Given three vertices of a rectangle, students will find the coordinates of the fourth vertex.
www.iit.edu /~smile/ma9214.html   (254 words)

  
 1.3 Polar Coordinates in the Plane   (Site not responding. Last check: 2007-11-07)
Figure 1: Among the possible sets of polar coordinates for P are: (10, 30°), (10, 390°) and (10, -330°).
Among the sets of polar coordinates for Q are: (2.5, 210°) and (-2.5, 30°).
Consider a system of polar coordinates and a system of cartesian coordinates with the same origin.
www.geom.uiuc.edu /docs/reference/CRC-formulas/node5.html   (183 words)

  
 Cartesian coordinates
In rectangular coordinates, the type most often used, the axes are taken to be perpendicular, with the
In oblique coordinates the axes are not perpendicular; the abscissa of
Cartesian Data announces breakthrough in data storage technology for higher capacity, low cost mobile applications; new company's proprietary TMT technology offers alternative to conventional disk drive and FLASH memory architectures.
www.infoplease.com /ce6/sci/A0810636.html   (383 words)

  
 Cartesian Coordinate System   (Site not responding. Last check: 2007-11-07)
This lesson is designed to familiarize students to the Cartesian Coordinate System and its many uses in the world of mathematics.
The Cartesian coordinate system was developed by the mathematician Descartes during an illness.
To show students that the coordinate plane is useful in more than just describing the location of objects lead a discussion on reading points off a graph.
www.shodor.org /interactivate/lessons/cartesian.html   (682 words)

  
 Drawing plane and coordinate system - maths online Gallery
is a simple dynamical diagram illustrating the relation between the position of a point in the drwaing plane and its (cartesian) coordinates.
A sample of coordinate lines may be switched on and off.
A sample of coordinate lines may be switched on and off, thus illustrating the fact that oblique coordinates give rise to a "grid" on the drawing plane different from that related to cartesian (rectangular) coordinates.
www.univie.ac.at /future.media/moe/galerie/zeich/zeich.html   (227 words)

  
 World Web Math: Vector Calculus: Cartesian Coordinates
Now that we have an oriented coordinate axis system, we can convert points to triplets simply by projecting the point onto each of our axes.
These numbers are called the cartesian coordinates of P, and every point has a unique triplet of cartesian coordinates.
It would be hard to overstate the importance of Cartesian coordinates in the history (and practice) of mathematics.
web.mit.edu /wwmath/vectorc/3d/cartesian.html   (635 words)

  
 9.2 Cylindrical Coordinates in Space   (Site not responding. Last check: 2007-11-07)
To define cylindrical coordinates, we take an axis (usually called the z-axis) and a perpendicular plane, on which we choose a ray (the initial ray) originating at the intersection of the plane and the axis (the origin).
) of the projection of P on the plane, and the coordinate z of the projection of P on the axis (Figure 1).
,z) of cylindrical coordinates for P are (10,30°,5) and (10,390°,5).
www.geom.uiuc.edu /docs/reference/CRC-formulas/node40.html   (110 words)

  
 1.2 Cartesian Coordinates in the Plane   (Site not responding. Last check: 2007-11-07)
In cartesian coordinates (or rectangular coordinates), the ``address'' of a point P is given by two real numbers indicating the positions of the perpendicular projections from the point to two fixed, perpendicular, graduated lines, called the axes.
If one coordinate is denoted x and the other y, the axes are called the x-axis and the y-axis, and we write P=(x,y).
The axes divide the plane into four quadrants: P is in the first quadrant, Q in the second, R in the third, and S in the fourth.
www.geom.umn.edu /docs/reference/CRC-formulas/node4.html   (150 words)

  
 [No title]
We can hypothesise that this pathway is one geometric representation of the minimum physiological connectedness needed for the coordinated structural development of the asexual reproduction mechanism in fungi.
The x- and y- locational coordinates of each spore, and a total count of the number of spores was determined using Colour Freelance Image Analysis software (Sight Systems; Berks., U.K., ver 1.16, 1991).
The centroid pair-listing of x and y coordinates for each spore position was used to evaluate the MST for each image.
www.swin.edu.au /chem/bio/fractals/mst01.htm   (4114 words)

  
 Cartesian coordinates - OneLook Dictionary Search
Cartesian coordinates : Compact Oxford English Dictionary [home, info]
Cartesian coordinates : Columbia Encyclopedia, Six Edition [home, info]
Words similar to Cartesian coordinates: cartesian coordinate, more...
www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=Cartesian+coordinates   (182 words)

  
 Polar Coordinates   (Site not responding. Last check: 2007-11-07)
For circular motion, it is possible (but quite inconvenient) to use the cartesian coordinates we have relied on during the previous sections.
Instead of describing the position of an object using x and y coordinates, this system uses two coordinates that locate the object's position using its distance from the origin (called "r" for radius) and its angle (theta) from the positive x-axis.
The only coordinate that changes is the angle theta, which varies as a relatively simple function of time.
www.physics.isu.edu /~keeter/phys211dir/quiz7/pg1th2.htm   (284 words)

  
 Cartesian Shift Coordinates   (Site not responding. Last check: 2007-11-07)
If the process topology is a cartesian structure, a MPI_SENDRECV operation is likely to be used along a coordinate direction to perform a shift of data.
The direction argument indicates the dimension of the shift, i.e., the coordinate which value is modified by the shift.
Depending on the periodicity of the cartesian group in the specified coordinate direction, MPI_CART_SHIFT provides the identifiers for a circular or an end-off shift.
www.mpi-forum.org /docs/mpi-11-html/node137.html   (360 words)

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