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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.)
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
There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics).
Mathematics and Medicine in Sanskrit. pp. 37– 62. Bryant, Edwin (2001). The Quest for the Origins of Vedic Culture: The Indo-Aryan Migration Debate. Oxford University Press. ISBN 9780195137774. Cooke, Roger (2005) [First published 1997]. The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0-471-44459-6. Datta, Bibhutibhushan ...
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or ...
It also differs from the approach taken in Menelaus' Spherics, a treatise of the same title written 3 centuries later, which treats the geometry of the sphere intrinsically, analyzing the inherent structure of the spherical surface and circles drawn on it rather than primarily treating it as a surface embedded in three-dimensional space.
9th century - Thābit ibn Qurra discusses the quadrature of the parabola and the volume of different types of conic sections. [5] 12th century - Bhāskara II discovers a rule equivalent to Rolle's theorem for , 14th century - Nicole Oresme proves of the divergence of the harmonic series,