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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.
For instance, Leonia High School, which incorporated grades 8–12 (since there was no middle school then), called the program "Math X" for experimental, with individual courses called Math 8X, Math 9X, etc. [13] Hunter College High School used it as the basis for its Extended Honors Program; the school's description stated that the program ...
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 high-water mark of Chinese mathematics occurred in the 13th century during the latter half of the Song dynasty (960–1279), with the development of Chinese algebra. The most important text from that period is the Precious Mirror of the Four Elements by Zhu Shijie (1249–1314), dealing with the solution of simultaneous higher order ...
This is a timeline of pure and applied mathematics history.It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic ...
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. [1]
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 ...