For instance, we might know that in non-Euclidean geometries, parallels meet.
But they constitute the substance of non-Euclidean geometry; they are its blood and sinews.
The real basis of the non-Euclidean geometry is dimension as direction.
In their non-Euclidean geometry the part is always greater than the whole.
Beltrami's mathematical investigations were devoted mainly to the non-Euclidean geometry.
The term "non-Euclidean" is used to designate any system of geometry which is not strictly Euclidean in content.
It involves the theory of non-Euclidean geometry, Euclid's postulate of parallels being used in proving this theorem.
On this postulate hang all the "law and the prophets" of the non-Euclidean Geometry.
A special application of his theory of continuous groups was to the general problem of non-Euclidean geometry.
Lobachevski has proved not, by creating non-Euclidean geometry.
non-Euclidean Relating to any of several modern geometries that are based on a set of postulates other than the set proposed by Euclid, especially one in which all of the postulates of Euclidean geometry hold except the parallel postulate. Compare Euclidean. |