Euklidisch

Euklidisch is the German adjective meaning "Euclidean" and is used to describe concepts, objects, or methods associated with the ancient Greek mathematician Euclid or with Euclid's axiomatic framework, particularly in geometry and number theory.

In geometry, euklidisch denotes properties that satisfy Euclid's postulates, especially the parallel postulate, and applies to Euclidean space of any finite dimension. It underpins the standard notions of distance, angle, and congruence, such as the Euclidean distance and the Euclidean plane or space.

In number theory, the term can refer to methods developed by Euclid, most notably the Euclidean algorithm for computing the greatest common divisor. German mathematical texts commonly designate these processes as "euklidisch" or "euklidischer Algorithmus."

Outside strict Euclidean geometry, the term serves to contrast with non-Euclidean geometries in which the parallel postulate fails. In such contexts, "euklidisch" designates objects or theorems that behave according to Euclid's framework.

Originating from the name Euclid (Latin Euclides), the adjective "euklidisch" is the German term for anything pertaining to Euclid or Euclidean geometry.