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  2. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    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.

  3. Euclid and His Modern Rivals - Wikipedia

    en.wikipedia.org/wiki/Euclid_and_his_Modern_Rivals

    Euclid and His Modern Rivals is a mathematical book published in 1879 by the English mathematician Charles Lutwidge Dodgson (1832–1898), better known under his literary pseudonym "Lewis Carroll". It considers the pedagogic merit of thirteen contemporary geometry textbooks , demonstrating how each in turn is either inferior to or functionally ...

  4. Euclid - Wikipedia

    en.wikipedia.org/wiki/Euclid

    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.

  5. List of geometers - Wikipedia

    en.wikipedia.org/wiki/List_of_geometers

    One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to c. 100 AD . The diagram accompanies Book II, Proposition 5. The diagram accompanies Book II, Proposition 5.

  6. Euclidean planes in three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Euclidean_planes_in_three...

    In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is the empty set if the line is parallel to the plane but outside it.

  7. Euclid's Elements - Wikipedia

    en.wikipedia.org/wiki/Euclid's_Elements

    Euclid's axiomatic approach and constructive methods were widely influential. Many of Euclid's propositions were constructive, demonstrating the existence of some figure by detailing the steps he used to construct the object using a compass and straightedge. His constructive approach appears even in his geometry's postulates, as the first and ...

  8. Tarski's axioms - Wikipedia

    en.wikipedia.org/wiki/Tarski's_axioms

    Hilbert's axioms for plane geometry number 16, and include Transitivity of Congruence and a variant of the Axiom of Pasch. The only notion from intuitive geometry invoked in the remarks to Tarski's axioms is triangle. (Versions B and C of the Axiom of Euclid refer to "circle" and "angle," respectively.) Hilbert's axioms also require "ray ...

  9. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    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.

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