Cartesische

Cartesische is a Dutch adjective meaning Cartesian. It is used to describe concepts associated with René Descartes and his influence across mathematics, philosophy, and related fields. In Dutch-language texts, cartesiaanse coördinaten, cartesiaans vlak and other phrases reflect this root.

In mathematics, cartesiaanse coördinaten refer to a coordinate system in which points in a plane or space are defined by ordered pairs or triples (x, y, z). This framework, introduced by Descartes in the 17th century, underpins analytic geometry and the translation of algebraic equations into geometric form. The Cartesian plane consists of a horizontal x-axis and a vertical y-axis, with the three-dimensional extension adding a z-axis. This system enables calculations of distance, slope, and transformations within a coordinate framework.

In set theory and logic, cartesiaanse product (Cartesian product) denotes the product of sets, such as A × B, the set of all ordered pairs (a, b) with a in A and b in B. The concept is foundational in mathematics and appears in computer science and related disciplines under variations of the same term in different languages.

In philosophy, Cartesianism (cartesiaanse filosofie) refers to the school of thought associated with Descartes, including methodological doubt, rationalism, and the mind–body problem. Key ideas include the cogito argument and the development of a systematic approach to knowledge, science, and epistemology. Cartesian influence helped shape early modern science and debates on certainty, representation, and dualism.

The term appears with cognates in other languages, such as Cartesian (English), kartesisch (German), and cartésien (French), but remains closely tied to Descartes’ legacy in scholarly usage.