affine geometry hendese-ye karvan Fr.: géométrie affine The study of the properties which are → invariant under → affine transformations. |
analytic geometry hendese-ye ânâlasi Fr.: géométrie analytique The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. |
differential geometry hendese-ye degarsâneyi Fr.: géométrie différentielle The study of curved spaces using differential calculus. → differential; → geometry. |
Euclidean 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. |
geometry hendesé (#) Fr.: géométrie 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," |
non-Euclidean geometry 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. |
Riemann's geometry hendese-ye Riemann Fr.: géométrie de Riemann Same as → Riemannian geometry. → Riemannian; → geometry. |
Riemannian geometry hendese-ye Riemanni 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. |
spherical geometry hendese-ye kore-yi 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. |