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1870 – Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate, 1873 – Charles Hermite proves that e is transcendental, 1878 – Charles Hermite solves the general quintic equation by means of elliptic and modular functions
Download as PDF; Printable version; ... Pages in category "History of geometry" ... This page was last edited on 6 January 2023, ...
In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)
Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest of these was Non-Euclidean geometry, which considers spaces where Euclid's parallel postulate fails. Saccheri first studied this geometry in 1733. Lobachevsky, Bolyai, and Riemann developed the subject further 100 years ...
A History of Greek Mathematics: vol. 1, vol. 2; The Works of Archimedes. Archimedes' Quadrature Of The Parabola; Archimedes' On The Measurement Of The Circle; Diophantus Of Alexandria: A Study In The History Of Greek Algebra; The Thirteen Books of Euclid's Elements: vol. 1, vol. 2, vol. 3
After teaching mathematics at a number of schools, he was appointed to the chair of mathematics at Auckland University College in New Zealand in 1933. He was very critical of the state of the New Zealand curriculum and set about writing a series of well received textbooks .
On p. 139 Guggenheimer sums up the field by noting, "A Klein geometry is the theory of geometric invariants of a transitive transformation group (Erlangen program, 1872)". Thomas Hawkins (1984) "The Erlanger Program of Felix Klein: Reflections on Its Place In the History of Mathematics", Historia Mathematica 11:442–70.
Saccheri is primarily known today for his last publication, in 1733 shortly before his death. Now considered an early exploration of non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami, in the mid-19th century.
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