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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 ( theorems ) from these.

  3. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

  4. Euclid's Elements - Wikipedia

    en.wikipedia.org/wiki/Euclid's_Elements

    Book 6 applies proportions to plane geometry, especially the construction and recognition of similar figures. Book 7 deals with elementary number theory: divisibility, prime numbers and their relation to composite numbers, Euclid's algorithm for finding the greatest common divisor, finding the least common multiple.

  5. 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.

  6. Euclid's Data - Wikipedia

    en.wikipedia.org/wiki/Euclid's_Data

    Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Data (Greek: Δεδομένα, Dedomena) is a work by Euclid. It deals with the ...

  7. Pasch's axiom - Wikipedia

    en.wikipedia.org/wiki/Pasch's_axiom

    Pasch's axiom — Let A, B, C be three points that do not lie on a line and let a be a line in the plane ABC which does not meet any of the points A, B, C.If the line a passes through a point of the segment AB, it also passes through a point of the segment AC, or through a point of segment BC.

  8. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. = + In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

  9. Butterfly theorem - Wikipedia

    en.wikipedia.org/wiki/Butterfly_theorem

    The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows: [1]: p. 78 Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.

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