Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
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In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.
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Cartesian plane coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more.
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Cartesian plane coordinates are essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more.
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Adjective Cartesian plane refers to the French mathematician and philosopher Rene Descartes, who published this idea in 1637 while he was resident in the Netherlands.
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Development of the Cartesian plane coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz.
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Cartesian plane coordinate system in two dimensions is defined by an ordered pair of perpendicular lines, a single unit of length for both axes, and an orientation for each axis.
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Cartesian plane coordinate system for a three-dimensional space consists of an ordered triplet of lines that go through a common point, and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all three axes.
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Alternatively, each coordinate of a point P can be taken as the distance from P to the hyperCartesian plane defined by the other two axes, with the sign determined by the orientation of the corresponding axis.
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Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is, with the Cartesian product, where is the set of all real numbers.
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Similarly, a three-dimensional Cartesian plane system defines a division of space into eight regions or octants, according to the signs of the coordinates of the points.
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All affine transformations of the Cartesian plane can be described in a uniform way by using matrices.
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Cartesian plane'saring transformation will push the top of a square sideways to form a parallelogram.
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Regardless of the rule used to orient the Cartesian plane, rotating the coordinate system will preserve the orientation.
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The standard orientation, where the xy-Cartesian plane is horizontal and the z-axis points up is called right-handed or positive.
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The red circle is parallel to the horizontal xy-Cartesian plane and indicates rotation from the x-axis to the y-axis .
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Cartesian plane coordinates are an abstraction that have a multitude of possible applications in the real world.
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