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Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father. Carl Friedrich Gauss, on reading the Appendix, wrote in a letter, "I regard this young geometer Bolyai as a genius of the first order." [7] To his old friend Farkas Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the ...
In the 19th century, hyperbolic geometry was explored extensively by Nikolai Lobachevsky, János Bolyai, Carl Friedrich Gauss and Franz Taurinus. Unlike their predecessors, who just wanted to eliminate the parallel postulate from the axioms of Euclidean geometry, these authors realized they had discovered a new geometry. [11] [12]
Hyperbolic space, developed independently by Nikolai Lobachevsky, János Bolyai and Carl Friedrich Gauss, is a geometric space analogous to Euclidean space, but such that Euclid's parallel postulate is no longer assumed to hold. Instead, the parallel postulate is replaced by the following alternative (in two dimensions):
Though they were largely ignored during their lifetimes, János Bolyai's groundbreaking work on hyperbolic geometry would later be recognized as foundational to modern mathematics. Farkas Bolyai had studied at Göttingen from 1796 to 1799, where he formed a lasting friendship with Carl Friedrich Gauss.
This is an accepted version of this page This is the latest accepted revision, reviewed on 4 January 2025. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...
In 1831, János Bolyai included, in a book by his father, an appendix describing acute geometry, which, doubtlessly, he had developed independently of Lobachevsky. Carl Friedrich Gauss had also studied the problem, but he did not publish any of his results. Upon hearing of Bolyai's results in a letter from Bolyai's father, Farkas Bolyai, Gauss ...
Gauss mentioned to Bolyai's father, when shown the younger Bolyai's work, that he had developed such a geometry several years before, [11] 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 ...
Gauss mentioned to Bolyai's father, when shown the younger Bolyai's work, that he had developed such a geometry several years before, [64] 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 ...