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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 ...
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.
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
The converse may or may not be true, and even if true, the proof may be difficult. 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.
Conversion (the converse), "If I wear my coat, then it is raining ." The converse is actually the contrapositive of the inverse, and so always has the same truth value as the inverse (which as stated earlier does not always share the same truth value as that of the original proposition).
Hinge has found that daters prefer voice prompts as a way to get to know a person better before meeting up in real life. To add a voice prompt, go to your profile and find it underneath the photo ...
Theorem. [2] [3] If a framework is infinitesimally rigid, then it is rigid. The converse of this theorem is not true in general; however, it is true for generic rigid frameworks (with respect to infinitesimal rigidity), see combinatorial characterizations of generically rigid graphs.