Euklidean

Euklidean is a term derived from the name of the ancient Greek mathematician Euclid. It most commonly refers to Euclidean geometry, also known as plane geometry, which is the mathematical system based on the axioms and postulates laid down by Euclid in his work "Elements" around 300 BCE. This system describes the properties of space and shapes in two and three dimensions using concepts like points, lines, planes, and angles. Key principles include the parallel postulate, which states that for any given line and a point not on that line, there is exactly one line through the point parallel to the given line.

The term Euklidean can also be used more broadly to describe anything that adheres to or is derived from the principles of Euclidean geometry. For instance, an Euklidean space is a geometric space where the distance between two points is measured using the standard Euclidean distance formula, which is a generalization of the Pythagorean theorem. In fields like physics and computer graphics, Euklidean concepts are fundamental for describing physical space and representing objects. Non-Euclidean geometries, which deviate from Euclid's postulates, particularly the parallel postulate, exist and are crucial in areas such as general relativity. Therefore, "Euklidean" typically signifies a system or concept that is consistent with the foundational rules established by Euclid's geometric framework.