Cartesian coordinate system
Introduction
The Cartesian coordinate system is a mathematical concept used to represent points in a certain space. It is named after the French mathematician Descartes, who introduced this system in the 17th century. The system uses two or more numbers (coordinates) to uniquely determine the location of a point in the space.
Concept and Definition
In a Cartesian coordinate system, each point is specified by a set of numerical coordinates, which are the signed distances from the point to fixed perpendicular oriented lines, known as axes. The simplest example of a Cartesian coordinate system is the identification of points in the Euclidean plane with pairs of real numbers (x, y).
Mathematical Formulation
In a two-dimensional Cartesian coordinate system, a point P in the plane is identified by an ordered pair of numbers (x, y), where x is the distance from P to the vertical axis (often called the y-axis), and y is the distance from P to the horizontal axis (often called the x-axis). The signs of the coordinates indicate on which side of the axes the point lies.
In a three-dimensional Cartesian coordinate system, a point P in space is identified by an ordered triple of numbers (x, y, z), where x, y, and z are the distances from P to three mutually perpendicular planes. The signs of the coordinates indicate on which side of the planes the point lies.
Applications
The Cartesian coordinate system is used in a wide range of fields, including physics, engineering, computer graphics, and geography. It is also fundamental to the study of mathematics, particularly calculus and linear algebra.