Home›Geometry›Statement Form›CharacterizationConceptCharacterizationLogic, Foundations and Set TheoryReference and ClassificationDevelopingIn mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. The cited article explains that to say a property characterizes an object is to say that not only does the object have the property, but that it is the only thing that has it, and that even though a characterization identifies an object uniquely, several characterizations can exist for a single object. It notes the common phrasings that a property is necessary and sufficient for the object, or that the object holds if and only if the property does. Theorems stated as if and only if conditions are grouped under this concept.CharacterizationConnectionsSourcesTake a Related QuizComments (0)Reader Challenges (0)CharacterizationFilter Results29 entriesBranchAllAlgebra (1)Algebraic Geometry (3)Differential Geometry (1)Discrete Geometry (2)Geometry (23)Topic AreaAllAlgebraic Geometry (3)Classical Euclidean Geometry (6)Convex and Discrete Geometry (3)Differential Geometry (3)Projective Geometry (3)Triangle and Circle Geometry (11)ProvedAll1640 (1)1648 (1)1672 (1)1678 (1)1731 (1)1796 (1)1797 (1)1799 (1)1807 (1)1827 (1)1833 (1)1881 (1)1898 (1)1899 (1)1931 (1)1949 (1)1953 (1)Proved ByAllArthur Cayley (1)Blaise Pascal (1)Carl Friedrich Gauss (2)Euclid (1)Frank Morley (1)Gaspard Monge (1)Giovanni Ceva (1)Heinz Hopf (1)Jakob Steiner (2)Pierre Varignon (1)Robert Simson (1)Wei-Liang Chow (1)Willi Rinow (1)William Vallance Douglas Hodge (1)Élie Cartan (1)Named AfterAllCarl Friedrich Gauss (1)Show ResultsBrowseCompareSelect all 29Beckman-Quarles TheoremCharacterizationBrianchon's TheoremCharacterizationCartan-Hadamard TheoremCharacterizationCayley-Bacharach TheoremCharacterizationCeva's TheoremCharacterizationChow's TheoremCharacterizationClifford's Circle TheoremsCharacterizationConstructibility of the Regular HeptadecagonCharacterizationCrystallographic Restriction TheoremCharacterizationDesargues' TheoremCharacterizationEqual Incircles TheoremCharacterizationGauss's Theorema EgregiumCharacterizationHodge Index TheoremCharacterizationHopf-Rinow TheoremCharacterizationIsoperimetric InequalityCharacterizationJapanese Theorem for Cyclic PolygonsCharacterizationKawasaki's TheoremCharacterizationMiquel's TheoremCharacterizationMohr-Mascheroni TheoremCharacterizationMonge's TheoremCharacterizationMorley's Trisector TheoremCharacterizationNapoleon's TheoremCharacterizationPascal's TheoremCharacterizationPoncelet-Steiner TheoremCharacterizationSimson Line TheoremCharacterizationSteiner-Lehmus TheoremCharacterizationThales' TheoremCharacterizationVarignon's TheoremCharacterizationWallace-Bolyai-Gerwien TheoremCharacterizationConnectionsIn BranchLogic and Foundations, Branches of Mathematics Well-attested Source Wolfram MathWorld: CharacterizationStatement Form OfRiemann Rearrangement Theorem, Theorems Well-attested Riemann-Lebesgue Lemma, Theorems Well-attested Riemann's Removable Singularity Theorem, Theorems Well-attested Rising Sun Lemma, Theorems Well-attested Robbins' Theorem, Theorems Well-attested Robertson-Seymour Theorem, Theorems Well-attested Robin's Theorem, Theorems Well-attested Robinson's Joint Consistency Theorem, Theorems Well-attested Rouche-Capelli Theorem, Theorems Well-attested Rybczynski Theorem, Theorems Well-attested Sahlqvist Correspondence Theorem, Theorems Well-attested Sard's Theorem, Theorems Well-attested Sato-Tate Theorem, Theorems Well-attested Schnyder's Theorem, Theorems Well-attested Shapley's Theorem, Theorems Well-attested Sharp-P-Completeness of 01-Permanent, Theorems Well-attested Siegel-Walfisz Theorem, Theorems Well-attested Simson Line Theorem, Theorems Well-attested Sipser-Lautemann Theorem, Theorems Well-attested Skolem-Mahler-Lech Theorem, Theorems Well-attested Slutsky's Theorem, Theorems Well-attested Sobolev Embedding Theorem, Theorems Well-attested Soundness Theorem, Theorems Well-attested Space Hierarchy Theorem, Theorems Well-attested Specht's Theorem, Theorems Well-attested Spin-Statistics Theorem, Theorems Well-attested Stark-Heegner Theorem, Theorems Well-attested Steiner-Lehmus Theorem, Theorems Well-attested Steinitz's Theorem (Convex Polytopes), Theorems Well-attested Stolper-Samuelson Theorem, Theorems Well-attested Strong Law of Large Numbers, Theorems Well-attested Strong Perfect Graph Theorem, Theorems Well-attested Structure Theorem for Gaussian Measures, Theorems Well-attested Tarski-Seidenberg Theorem, Theorems Well-attested Taylor-Proudman Theorem, Theorems Well-attested Tennis Racket Theorem, Theorems Well-attested Thales' Theorem, Theorems Well-attested Thurston's Geometrization Theorem, Theorems Well-attested Toda's Theorem, Theorems Well-attested Topkis's Theorem, Theorems Well-attested Tunnell's Theorem, Theorems Well-attested Tutte's Theorem (Graph Theory), Theorems Well-attested Tychonoff's Theorem, Theorems Well-attested Urysohn's Lemma, Theorems Well-attested Utility Representation Theorem, Theorems Well-attested Uzawa's Theorem, Theorems Well-attested Van Kampen's Theorem, Theorems Well-attested Vantieghem's Theorem, Theorems Well-attested Varignon's Theorem, Theorems Well-attested Vickrey-Clarke-Groves Theorem, Theorems Well-attested Showing 201 to 250 of 262 in Statement Form Of, page 5 of 6.← Previous1…3456Next →SourcesCharacterizationWikipedia, lead sectionQuote, Wikipedia, lead sectionIn mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it.View the SourceWolfram MathWorld: CharacterizationWolfram MathWorldIn Branch: Logic and Foundations, Subject classificationsQuote, In Branch: Logic and Foundations, Subject classificationsFoundations of Mathematics Theorem ProvingView the SourceTake a Related QuizOrigins of Mathematical ConceptsCovers this kind of entry.Comments (0)No comments yet. 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