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  2. 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 ]

  3. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Jacobson–Morozov theorem (Lie algebra) Japanese theorem for concyclic polygons (Euclidean geometry) Japanese theorem for concyclic quadrilaterals (Euclidean geometry) John ellipsoid ; Jordan curve theorem ; Jordan–Hölder theorem (group theory) Jordan–Schönflies theorem (geometric topology) Jordan–Schur theorem (group theory)

  4. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    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] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]

  5. Ptolemy's inequality - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_inequality

    For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...

  6. List of mathematical logic topics - Wikipedia

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

    Soundness theorem; 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 ...

  7. 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 .

  8. Hierarchy (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Hierarchy_(mathematics)

    The term hierarchy is used to stress a hierarchical relation among the elements. Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where n ≤ n ′ {\displaystyle n\leq n'} whenever we can find some other number m {\displaystyle m} so ...

  9. Happy ending problem - Wikipedia

    en.wikipedia.org/wiki/Happy_ending_problem

    Theorem — for any positive integer N, any sufficiently large finite set of points in the plane in general position has a subset of N points that form the vertices of a convex polygon. The proof appeared in the same paper that proves the Erdős–Szekeres theorem on monotonic subsequences in sequences of numbers.

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