User:Jeffwang/Cartesian coordinate system
From Wikipedia, the free encyclopedia
All basis of this page is from the English Wikipedia.
A Cartesian coordinate system specifies each and every point in a plane by a pair of numerical coordinates, which are the signed distances (positive and negative number signs) from the point to two fixed right-angular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is it's origin, usually at ordered pair (0,0). The coordinates can also be defined as the positions of the right-angular projections of the point onto the two axes, expressed as signed distances from the origin.
One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three connected right-angular planes (or also by its right-angular projection onto three connected right-angular lines). In general, one can specify a point in a space of any dimension n by use of n Cartesian coordinates, the signed distances from n mutually perpendicular hyperplanes.
The invention of Cartesian coordinates in the 17th century by René Descartes (Name translated/changed into Latin: Cartesius) made mathematics on a higher level by providing the first smooth link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle that has a radius of 2 may be said as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
Cartesian coordinates are the base of analytic geometry, and provide interesting geometric explanations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multiple variable calculus, group theory, and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied categories that deal with geometry, including astronomy, physics, engineering, and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design, and other geometry-related data processing.
Above: Ready for Simple Wikipedia
Below: Not yet ready for Simple Wikipedia