Kartesiusjärjestelmän

Kartesiusjärjestelmä, often referred to as the Cartesian coordinate system, is a fundamental concept in mathematics that provides a way to uniquely define the position of a point in a plane or in space. It was developed by the French mathematician and philosopher René Descartes in the 17th century.

The system is based on two or three perpendicular axes. In a two-dimensional plane, these are typically labeled the x-axis and the y-axis. The x-axis is usually horizontal, and the y-axis is vertical. The point where these axes intersect is called the origin, and it has coordinates (0,0).

To locate a point in this system, two numbers, called coordinates, are used. The first coordinate, the x-coordinate or abscissa, indicates the distance of the point from the y-axis along the x-axis. A positive x-value means the point is to the right of the origin, and a negative x-value means it is to the left. The second coordinate, the y-coordinate or ordinate, indicates the distance of the point from the x-axis along the y-axis. A positive y-value means the point is above the origin, and a negative y-value means it is below. A point is represented as an ordered pair (x, y).

In three-dimensional space, a third axis, the z-axis, is added, which is perpendicular to both the x and y axes. This allows for the specification of a point's position using an ordered triplet (x, y, z). The Cartesian coordinate system is crucial for graphing functions, solving geometric problems, and is the basis for many advanced mathematical and scientific disciplines.