Of or pertaining to Euclid, or his postulates. → Euclidean division, → Euclidean geometry, → Euclidean space, → non-Euclidean geometry.
After the Gk. geometrician and educator at Alexandria, around 300 B.C., who applied the deductive principles of logic to geometry, thereby deriving statements from clearly defined axioms.
Fr.: division euclidienne
In arithmetic, the conventional process of division of two → integers. For a → real number a divided by b > 0, there exists a unique integer q and a real number r, 0 ≤ r <b, such that a = qb + r.
hendese-ye Oqlidosi (#)
Fr.: géométrie euclidienne
The geometry based on the postulates or descriptions of Euclid. One of the critical assumptions of the Euclidean geometry is given in his fifth postulate: through a point not on a line, one and only one line be drawn parallel to the given line. See also → non-Euclidean geometry.
Fr.: espace euclidean
A space in which the → distance between any two points is given by the → Pythagorean theorem: d2 = (Δx)2 + (Δy)2 + (Δz)2, where d is distance and Δx, Δy, and Δz are differential → Cartesian coordinates. Euclidean n-space Rn is the set of all column vectors with n real entries.
hendese-ye nâ-oqlidosi (#)
Fr.: géométrie non-euclidienne
Any of several geometries which do not follow the postulates and results of Euclidean geometry. For example, in a non-Euclidean geometry through a point several lines can be drawn parallel to another line. Or, the sum of the interior angles of a triangle differs from 180 degrees. According to Einstein's general relativity theory, gravity distorts space into a non-Euclidean geometry.
→ non-; → Euclidean geometry.
Fr.: espace pseudo-euclidien
A real vector space of dimension n having a symmetric bilinear form (x, y) such that in some basis e1, ..., en, the quadratic form (x2) takes the form x12 + ... + xn - 12 - xn2. Such bases are called orthonormal.