Euclid of Alexandria, a Greek mathematician. / A male given name from Ancient Greek of mostly historical use. / A city in Ohio. / An unincorporated community in West Virginia.

Euclidean algorithm

(number theory) The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;

(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:

(mathematics, geometry) A space where the principles of Euclidean geometry apply.

plural of Euclidian space

Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.

(historical) Any of certain algorithms first described in Euclid's Elements.

(mathematics) the set of rigid motions that are also affine transformations.

(geometry) Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.