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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 ( theorems ) 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.
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.
The Euclidean algorithm was probably invented before Euclid, depicted here holding a compass in a painting of about 1474. The Euclidean algorithm is one of the oldest algorithms in common use. [27] It appears in Euclid's Elements (c. 300 BC), specifically in Book 7 (Propositions 1–2) and Book 10 (Propositions 2–3). In Book 7, the algorithm ...
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.
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 feature of the book that was most positively received by reviewers was its work extending results in distance and angle geometry to finite fields. Reviewer Laura Wiswell found this work impressive, and was charmed by the result that the smallest finite field containing a regular pentagon is F 19 {\displaystyle \mathbb {F} _{19}} . [ 1 ]
His Foundations of Euclidean Geometry (1927) was reviewed by F.W. Owens, who noted that 40 pages are devoted to "concepts of classes, relations, linear order, non archimedean systems, ..." and that order axioms together with a continuity axiom and a Euclidean parallel axiom are the required foundation. The object achieved is a "continuous and ...
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