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Geometry. 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 idealized ruler, known as a straightedge, is assumed ...
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint.
Euclid (/ ˈ j uː k l ɪ d /; 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 Elements (Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean ...
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 ]
There is a simple neusis construction using a marked ruler for a length which is the cube root of 2 times another length. [15] Mark a ruler with the given length; this will eventually be GH. Construct an equilateral triangle ABC with the given length as side. Extend AB an equal amount again to D. Extend the line BC forming the line CE.
Jean-Victor Poncelet (1788–1867) – projective geometry. Augustin-Louis Cauchy (1789–1857) August Ferdinand Möbius (1790–1868) – Euclidean geometry. Nikolai Ivanovich Lobachevsky (1792–1856) – hyperbolic geometry, a non-Euclidean geometry. Michel Chasles (1793–1880) – projective geometry.
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.