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Finally, in the 1920s, his interest turned to non-Euclidean geometry.
In this they were successful, thus creating the first non-Euclidean geometry.
He continued to do research on non-Euclidean geometry and taught in high schools for the next seven years.
For more information, see the history of non-Euclidean geometry.
He became known for his achievements in non-euclidean geometry.
The existence of these three types parallels the several non-Euclidean geometries.
Non-Euclidean geometry often makes appearances in works of science fiction and fantasy.
Between 1820 and 1823 he prepared a treatise on a complete system of non-Euclidean geometry.
Classical perspective and non-Euclidean geometry were not, after all, incompatible with one another.
In mathematics, hyperbolic space is a type of non-Euclidean geometry.
Discovery of the latter in 19th century was branded as the non-Euclidean geometry.
Non-Euclidean geometry is an example of a paradigm shift in the history of science.
It is a non-Euclidean geometry looking at hyperbolic space.
In non-Euclidean geometry, it is more common to talk about geodesics than (straight) lines.
For planar algebra, non-Euclidean geometry arises in the other cases.
Concepts like non-Euclidean geometry were once considered ill-behaved, but are now common objects of study.
"Have your studies led you into multidimensional non-Euclidean geometries?"
All of this was incredible, yet it had its own logic, like that of non-Euclidean geometry.
Essay on an interpretation of non-Euclidean geometry, 1868.
A version of the law of cosines also holds in non-Euclidean geometry.
Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century.
A simple non-euclidean geometry and its physical basis (1979)
He worked on the theories of linear differential equations, probability and non-euclidean geometry.
"Then you know that there are non-Euclidean geometries?"
In non-Euclidean geometry, straight lines are replaced with geodesics.