Creation of Non-Euclidean Geometry
The beginning of the 19th century would finally witness decisive steps in the creation of non-Euclidean geometry. Around 1830, the Hungarian mathematician János Bolyai and the Russian mathematician Nikolai Ivanovich Lobachevsky separately published treatises on hyperbolic geometry. Consequently, hyperbolic geometry is called Bolyai-Lobachevskian geometry, as both mathematicians, independent of each other, are the basic authors of non-Euclidean geometry. Gauss mentioned to Bolyai's father, when shown the younger Bolyai's work, that he had developed such a geometry several years before, though he did not publish. While Lobachevsky created a non-Euclidean geometry by negating the parallel postulate, Bolyai worked out a geometry where both the Euclidean and the hyperbolic geometry are possible depending on a parameter k. Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences.
Bernhard Riemann, in a famous lecture in 1854, founded the field of Riemannian geometry, discussing in particular the ideas now called manifolds, Riemannian metric, and curvature. He constructed an infinite family of geometries which are not Euclidean by giving a formula for a family of Riemannian metrics on the unit ball in Euclidean space. The simplest of these is called elliptic geometry and it is considered to be a non-Euclidean geometry due to its lack of parallel lines.
Read more about this topic: Non-Euclidean Geometry, History
Famous quotes containing the words creation of, creation and/or geometry:
“Poetry, at all times, exercises two distinct functions: it may reveal, it may unveil to every eye, the ideal aspects of common things ... or it may actually add to the number of motives poetic and uncommon in themselves, by the imaginative creation of things that are ideal from their very birth.”
—Walter Pater (18391894)
“Man is a masterpiece of creation if for no other reason than that, all the weight of evidence for determinism notwithstanding, he believes he has free will.”
—G.C. (Georg Christoph)
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (18031882)