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  2. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    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)

  3. Petr–Douglas–Neumann theorem - Wikipedia

    en.wikipedia.org/wiki/Petr–Douglas–Neumann...

    In geometry, the Petr–Douglas–Neumann theorem (or the PDN-theorem) is a result concerning arbitrary planar polygons.The theorem asserts that a certain procedure when applied to an arbitrary polygon always yields a regular polygon having the same number of sides as the initial polygon.

  4. Poncelet's closure theorem - Wikipedia

    en.wikipedia.org/wiki/Poncelet's_closure_theorem

    Illustration of Poncelet's porism for n = 3, a triangle that is inscribed in one circle and circumscribes another.. In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same ...

  5. 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 ...

  6. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]

  7. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    In Euclidean geometry, a regular polygon is a polygon that is direct equiangular ... This is a generalization of Viviani's theorem for the n = 3 case. [5] [6 ...

  8. Pick's theorem - Wikipedia

    en.wikipedia.org/wiki/Pick's_theorem

    In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [ 2 ]

  9. Similarity (geometry) - Wikipedia

    en.wikipedia.org/wiki/Similarity_(geometry)

    This rotational reduction is repeated, so the initial polygon is extended into an abyss of regular polygons. The center of the similarity is the common center of the successive polygons. A red segment joins a vertex of the initial polygon to its image under the similarity, followed by a red segment going to the following image of vertex, and so ...

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