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Compared to Euclidean geometry, hyperbolic geometry presents many difficulties for a coordinate system: the angle sum of a quadrilateral is always less than 360°; there are no equidistant lines, so a proper rectangle would need to be enclosed by two lines and two hypercycles; parallel-transporting a line segment around a quadrilateral causes ...
Indian mathematics emerged and developed in the Indian subcontinent [1] from about 1200 BCE [2] until roughly the end of the 18th century CE (approximately 1800 CE). In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava.
The East India Company thought that this project would take about five years, but it took nearly 70 years, well past the Indian Rebellion of 1857 and the end of company rule in India. Because of the extent of the land to be surveyed, the surveyors did not triangulate the whole of India but instead created what they called a "gridiron" of ...
150 BC – Jain mathematicians in India write the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations; 140 BC – Hipparchus develops the bases of trigonometry.
In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry).
Datta and Singh's 'History of Hindu Mathematics' should be in every library which reaches standards covered by the word "approved." It should be owned by individuals who have any interest whatever in the history of the progress of science. From the standpoint of authoritative subject matter and from that of book-making, it is a notable history ...
In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry. [1] It can also be related to the relativistic velocity addition formula. [2] [3]
He has widely published and presented his research in the area of hyperbolic manifolds and ending lamination spaces. His most notable work is the proof of existence of Cannon–Thurston maps . [ 9 ] [ 10 ] This led to the resolution of the conjecture that connected limit sets of finitely generated Kleinian groups are locally connected. [ 4 ]