Euklidske

Euklidske is an adjective used in Czech and other languages to describe concepts related to Euclid and his geometry. It often appears as euklidovské to denote Euclidean geometry and Euclidean space. The term derives from the Greek mathematician Euclid, who around 300 BCE authored Elements, an axiomatic presentation of geometry. In its classical form, Euklidske geometry studies points, lines, planes, and shapes in a flat (zero curvature) space, where the distance between two points is given by the Euclidean metric and the familiar notions of parallel lines, angles, and congruence apply. The central axioms, or postulates, include the idea that a straight line can be drawn between any two points and that given a line and a point not on it, there is exactly one parallel line through the point.

In modern mathematics, Euklidske geometry extends to n-dimensional Euclidean space, denoted R^n, equipped with the standard inner product and the induced distance. It provides the backdrop for much of classical physics, computer graphics, and engineering. The term contrasts with non-Euclidean geometries, where the parallel postulate is modified or replaced, leading to spherical or hyperbolic geometry. While non-Euclidean models describe curved spaces, Euklidske (Euclidean) geometry remains a foundational, locally flat approximation.

Additionally, the name appears in other contexts, such as the Euclidean algorithm in number theory, though that topic is separable from geometric use.