Axis (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 07/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Cartesian_coordinate_system


00:00:42 1 History
00:01:24 2 Description
00:01:45 2.1 One dimension
00:02:27 2.2 Two dimensions
00:03:10 2.3 Three dimensions
00:03:52 2.4 Higher dimensions
00:04:34 2.5 Generalizations
00:05:16 3 Notations and conventions
00:05:58 3.1 Quadrants and octants
00:06:40 4 Cartesian formulae for the plane
00:07:01 4.1 Distance between two points
00:08:04 4.2 Euclidean transformations
00:08:47 4.2.1 Translation
00:09:29 4.2.2 Rotation
00:10:12 4.2.3 Reflection
00:10:54 4.2.4 Glide reflection
00:11:37 4.2.5 General matrix form of the transformations
00:13:24 4.2.6 Affine transformation
00:14:49 4.2.7 Scaling
00:15:31 4.2.8 Shearing
00:16:13 5 Orientation and handedness
00:16:34 5.1 In two dimensions
00:17:17 5.2 In three dimensions
00:18:00 6 Representing a vector in the standard basis
00:19:03 7 Applications
00:19:46 8 See also
00:20:29 9 References
00:21:11 10 Sources
00:21:53 11 Further reading
00:22:35 12 External links



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SUMMARY
=======
A Cartesian coordinate system (UK: , US: ) is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular 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 mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) 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.

The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic 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 of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
Cartesian 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. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines 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.