Hyperbolic geometers

Hyperbolic geometers are mathematicians or researchers who specialize in hyperbolic geometry, which is a non-Euclidean geometry characterized by its unique properties and structures. In hyperbolic geometry, the parallel postulate of Euclidean geometry does not hold. Specifically, through a given point not on a line, there are infinitely many lines that do not intersect the given line, in contrast to Euclidean space, where there is exactly one such line.

Eugenio Beltrami (1835–1900) was an Italian mathematician known for his contributions to differential geometry and mathematical physics. He is particularly recognized for his work on non-Euclidean geometries, especially the development of models for hyperbolic geometry. Beltrami's work helped to provide a rigorous foundation for the theories established by mathematicians such as Nikolai Lobachevsky and János Bolyai, who independently developed hyperbolic geometry.

Ferdinand Minding does not appear to have significant recognition or established relevance in widely known fields, such as history, literature, science, or popular culture, based on the information available up to October 2023. It's possible that he could be a lesser-known figure, or the name might be relevant in a specific niche context.

János Bolyai (1802–1860) was a Hungarian mathematician known for his foundational work in non-Euclidean geometry. He is best known for developing the principles of hyperbolic geometry independently of the Russian mathematician Nikolai Lobachevsky. Bolyai's work demonstrated that it is possible to construct a consistent geometric system in which the parallel postulate of Euclidean geometry does not hold.

Nikolai Lobachevsky (1792–1856) was a Russian mathematician known primarily for his contributions to geometry, particularly for developing the concept of non-Euclidean geometry. He is often referred to as the "father of non-Euclidean geometry." Lobachevsky challenged the long-held assumption in Euclidean geometry that through any point not on a given line, there is exactly one line parallel to the given line.