kartézianus

Kartézianus refers to the Cartesian coordinate system and, more broadly, to the ideas associated with René Descartes that unite algebra and geometry. The term is named after the French philosopher-mathematician, whose work laid the foundation for analytic geometry. In many languages, kartézianus or its derivatives are used to describe Cartesian coordinates.

In the two-dimensional plane, a point is identified by an ordered pair (x, y), where x measures position along the horizontal axis and y along the vertical axis. The axes intersect at the origin (0, 0). Geometric objects can be described by equations: for example, a line by y = mx + b and general curves by F(x, y) = 0. This framework converts geometric problems into algebraic ones, enabling precise computation of distances, intersections, and areas.

The concept extends to three dimensions by introducing a z coordinate, giving points as (x, y, z) with the z-axis perpendicular to the x–y plane. It generalizes further to n dimensions with coordinates (x1, x2, ..., xn). The Cartesian product concept underlies this generalization, providing a systematic way to form tuples that locate points in higher-dimensional spaces.

Origins and impact: described in Descartes’ La Géométrie (1637), analytic geometry using Cartesian coordinates became central to calculus, physics, computer graphics, and engineering. It provides a universal language for describing lines, curves, surfaces, and transformations, and underpins many methods for solving geometric and algebraic problems.