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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.)
In the 1960s a new set of axioms for Euclidean geometry, suitable for American high school geometry courses, was introduced by the School Mathematics Study Group (SMSG), as a part of the New math curricula. This set of axioms follows the Birkhoff model of using the real numbers to gain quick entry into the geometric fundamentals.
ca. 1250 – Nasir Al-Din Al-Tusi attempts to develop a form of non-Euclidean geometry. 15th century – Nilakantha Somayaji, a Kerala school mathematician, writes the "Aryabhatiya Bhasya", which contains work on infinite-series expansions, problems of algebra, and spherical geometry
The American high-school geometry curriculum was eventually codified in 1912 and developed a distinctive American style of geometric demonstration for such courses, known as "two-column" proofs. [49] This remains largely true today, with Geometry as a proof-based high-school math class.
The School Mathematics Study Group (SMSG) was an American academic think tank focused on the subject of reform in mathematics education.Directed by Edward G. Begle and financed by the National Science Foundation, the group was created in the wake of the Sputnik crisis in 1958 and tasked with creating and implementing mathematics curricula for primary and secondary education, [1] which it did ...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term ...
1659 - Second edition of Van Schooten's Latin translation of Descartes' Geometry with appendices by Hudde and Heuraet, 1665 - Isaac Newton discovers the generalized binomial theorem and develops his version of infinitesimal calculus, 1667 - James Gregory publishes Vera circuli et hyperbolae quadratura, 1668 - Nicholas Mercator publishes ...