Fr.: géométrie affine
The study of the properties which are → invariant under → affine transformations.
Fr.: géométrie analytique
The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations.
Fr.: géométrie conforme
The study of the set of angle-preserving transformations on a space.
Fr.: géométrie différentielle
The study of curved spaces using differential calculus.
→ differential; → geometry.
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.
The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.
From O.Fr. géométrie, from L. geometria, from Gk. geometria "measurement of earth or land," from → geo- + -metria, from metrein "to measure," → -metry.
Hendesé, Mid.Pers. handâxtan "to measure," Manichean Mid.Pers. hnds- "to measure," Proto-Iranian ham-, → com-, + *das- "to heap, amass;" cf. Ossetic dasun/dast "to heap up;" Arm. loanword dasel "to arrange (a crowd, people)," das "order, arrangement,"
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.: géométrie de Riemann
Same as → Riemannian geometry.
→ Riemannian; → geometry.
Fr.: géométrie riemannienne
A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles of a → triangle is always greater than 180°. Riemannian figures can be thought of as figures constructed on a curved surface. The geometry is called elliptic because the section formed by a plane that cuts the curved surface is an ellipse.
→ Riemannian; → geometry.
Fr.: géométrie sphérique
The branch of geometry that deals with figures on the surface of a sphere (such as the spherical triangle and spherical polygon). It is an example of a non-Euclidean geometry.