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:

of, or relating to non-Euclidean geometry

(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.

(geometry) Adhering to the principles of traditional geometry, in which parallel lines are equidistant. / Of or relating to Euclid's Elements, especially to Euclidean geometry.

Of or relating to Euclidean zoning.

(geometry) The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.

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