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Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry. Klein proposed that group theory , a branch of mathematics that uses algebraic methods to abstract the idea of symmetry , was the most useful way of organizing geometrical knowledge; at the time it had already ...
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.
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 rigorous deductive methods of geometry found in Euclid's Elements of Geometry were relearned, and further development of geometry in the styles of both Euclid (Euclidean geometry) and Khayyam (algebraic geometry) continued, resulting in an abundance of new theorems and concepts, many of them very profound and elegant.
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described (although non-rigorously by modern standards) in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these.
Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics and control theory. Geometric mechanics applies principally to systems for which the configuration space is a Lie group , or a group of diffeomorphisms , or more ...
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