Euclidian

Euclidian is an adjective associated with Euclid of Alexandria, the ancient Greek mathematician, or with concepts and objects named after him. In modern technical writing, the standard spelling is Euclidean, but Euclidian appears in historical texts, some older publications, and certain niche or software-related contexts.

In mathematics, Euclidean geometry describes the plane, space, and figures studied through axioms attributed to Euclid. It emphasizes flat, or zero-curvature, geometry and forms the foundation for many geometric theorems and constructions. The term also appears in connection with Euclidean distance, a metric for measuring the straight-line separation between two points in n-dimensional space. This distance is computed as the square root of the sum of squared coordinate differences, generalizing the familiar Pythagorean theorem to higher dimensions. Euclidean space, typically denoted R^n, provides the natural setting for many problems in geometry, algebra, and analysis, equipped with the standard inner product that induces lengths and angles.

Another well-known Euclid-related concept is the Euclidean algorithm, a method for determining the greatest common divisor of two integers by repeated division. This algorithm is one of the oldest known algorithms and is foundational in number theory.

While Euclidean concepts remain central in classical geometry, many branches of geometry have since evolved into non-Euclidean frameworks. The distinction between Euclidean and non-Euclidean geometry is a key theme in the history of mathematics.

See also: Euclid, Euclidean geometry, Euclidean algorithm, Euclidian distance.