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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 compass.
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 ( theorems ) from these.
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.
Forum Geometricorum: A Journal on Classical Euclidean Geometry was a peer-reviewed open-access academic journal that specialized in mathematical research papers on Euclidean geometry. [ 1 ] Founded in 2001, it was published by Florida Atlantic University and was indexed by Mathematical Reviews [ 2 ] and Zentralblatt MATH . [ 3 ]
Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic with identity (i.e. is formulable as an elementary theory). As such, it does not require an underlying set theory. The only primitive objects of the system are "points" and the only primitive ...
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.
A useful method, due to Julius Plücker, creates a set of six coordinates as the determinants (<) from the homogeneous coordinates of two points (,,,) and (,,,) on the line. The Plücker embedding is the generalization of this to create homogeneous coordinates of elements of any dimension m {\displaystyle m} in a projective space of dimension n ...
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 ...
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