He did not grant independent existence to the non-euclidean geometries . 他不承認非歐幾里德幾何的獨立存在性。
The advent of the theory of relativity forced a drastic change in the attitude toward non-euclidean geometry . 相對論的發(fā)現(xiàn)迫使對待非歐幾里德幾何的態(tài)度有激烈的變化。
It was this concept that riemann generalized, thereby opening up new vistas in non-euclidean geometry . 這個概念嗣后為Riemann所推廣,從而在非歐幾里德幾何學中開辟了新前景。
But none of the mathematicians believed that these basic non-euclidean geometries would be physically significant . 但數(shù)學家們無人相信這些基本的非歐幾里德幾何必然有物理意義。
In mathematics, non-Euclidean geometry is a small set of geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is set aside.