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  2. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Jacobi's four-square theorem (number theory) Jacobson density theorem (ring theory) Jacobson–Bourbaki theorem ; Jacobson–Morozov theorem (Lie algebra) Japanese theorem for concyclic polygons (Euclidean geometry) Japanese theorem for concyclic quadrilaterals (Euclidean geometry) John ellipsoid ; Jordan curve theorem

  3. Euler's quadrilateral theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_quadrilateral_theorem

    Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .

  4. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8]

  5. List of mathematical logic topics - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_logic...

    Gödel's completeness theorem. Original proof of Gödel's completeness theorem; Compactness theorem; Löwenheim–Skolem theorem. Skolem's paradox; Gödel's incompleteness theorems; Structure (mathematical logic) Interpretation (logic) Substructure (mathematics) Elementary substructure. Skolem hull; Non-standard model; Atomic model ...

  6. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    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). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). [ 1 ]

  7. Constructible set (topology) - Wikipedia

    en.wikipedia.org/wiki/Constructible_set_(topology)

    They are used particularly in algebraic geometry and related fields. A key result known as Chevalley's theorem in algebraic geometry shows that the image of a constructible set is constructible for an important class of mappings (more specifically morphisms) of algebraic varieties (or more generally schemes). In addition, a large number of ...

  8. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    The latter sort of properties are called invariants and studying them is the essence of geometry. Thales' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Cantor supposed that Thales proved his theorem by means of Euclid ...

  9. Complete quadrangle - Wikipedia

    en.wikipedia.org/wiki/Complete_quadrangle

    A complete quadrangle (at left) and a complete quadrilateral (at right).. In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.