Search results
Results from the WOW.Com Content Network
The 19th century saw the development of the general concept of Euclidean space by Ludwig Schläfli, who extended Euclidean geometry beyond three dimensions. He discovered all the higher-dimensional analogues of the Platonic solids , finding that there are exactly six such regular convex polytopes in dimension four , and three in all higher ...
Evolution of Drafting Practices: Historically, advanced Euclidean geometry, including theorems like Pascal's theorem and Brianchon's theorem, was integral to drafting practices. However, with the advent of modern CAD systems, such in-depth knowledge of these theorems is less necessary in contemporary design and manufacturing processes.
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
Euclid (/ ˈ j uː k l ɪ d /; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. [2] Considered the "father of geometry", [3] he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.
The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry ...
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric ...
In the terms of Felix Klein's Erlangen programme, we read off from this that Euclidean geometry, the geometry of the Euclidean group of symmetries, is, therefore, a specialisation of affine geometry. All affine theorems apply. The origin of Euclidean geometry allows definition of the notion of distance, from which angle can then be deduced.
The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.