Introduction to the Cartesian Coordinate System
History:
The Cartesian coordinate system is named after René Descartes(1596-1650), the noted French mathematician and philosopher, who was among the first to describe its properties. However, historical evidence shows that Pierre de Fermat (1601-1665), also a French mathematician and scholar, did more to develop the Cartesian system than did Descartes.
The development of the Cartesian coordinate system enabled the development of perspective and projective geometry. It would later play an intrinsic role in the development of calculus by Isaac Newton andGottfried Wilhelm Leibniz.[3]
Nicole Oresme, a French philosopher of the 14th Century, used constructions similar to Cartesian coordinates well before the time of Descartes.
Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space.
Cartesian coordinate system:
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular 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 its origin. 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, 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.
Terms to remember:
Coordinate Axes
Three mutually perpendicular
The Cartesian coordinate system is named after René Descartes(1596-1650), the noted French mathematician and philosopher, who was among the first to describe its properties. However, historical evidence shows that Pierre de Fermat (1601-1665), also a French mathematician and scholar, did more to develop the Cartesian system than did Descartes.
The development of the Cartesian coordinate system enabled the development of perspective and projective geometry. It would later play an intrinsic role in the development of calculus by Isaac Newton andGottfried Wilhelm Leibniz.[3]
Nicole Oresme, a French philosopher of the 14th Century, used constructions similar to Cartesian coordinates well before the time of Descartes.
Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space.
Cartesian coordinate system:
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular 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 its origin. 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, 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.
Terms to remember:
Coordinate Axes
Three mutually perpendicular