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  2. Hinge theorem - Wikipedia

    en.wikipedia.org/wiki/Hinge_theorem

    The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...

  3. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle, and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.

  4. Moser's trick - Wikipedia

    en.wikipedia.org/wiki/Moser's_trick

    One implication holds by the invariance of the integral by diffeomorphisms: = = =. For the converse, we apply Moser's trick to the family of volume forms := +.Since () =, the de Rham cohomology class [] vanishes, as a consequence of Poincaré duality and the de Rham theorem.

  5. Converse theorem - Wikipedia

    en.wikipedia.org/wiki/Converse_theorem

    In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functions of various twists of it are well-behaved.

  6. Converse (logic) - Wikipedia

    en.wikipedia.org/wiki/Converse_(logic)

    For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3] In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context. That is, the converse of "Given P, if Q then R" will be "Given P, if R then Q".

  7. Give Your Hinge Matches Something to Respond to With These ...

    www.aol.com/lifestyle/95-hinge-prompt-answers...

    The app allows you to display three Hinge prompt answers, with a myriad of options to choose from (including voice and video prompts!). These range from funny, to deep, to nerdy.

  8. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.

  9. Hinge’s CEO insists the app doesn’t have an ‘attractiveness ...

    www.aol.com/finance/hinge-ceo-insists-app-doesn...

    Hinge’s parent company, which also owns Tinder, OkCupid, Match.com, The League, and more, disappointed investors last fall. Its third-quarter earnings showed a 6% year-over-year decline in ...