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 OfHerbrand's Theorem, Theorems Well-attested Herglotz's Variational Principle, Theorems Well-attested Hewitt-Savage Zero-One Law, Theorems Well-attested Hilbert's Nullstellensatz, Theorems Well-attested Hilbert-Speiser Theorem, Theorems Well-attested Hodge Index Theorem, Theorems Well-attested Hopf-Rinow Theorem, Theorems Well-attested Hurewicz Theorem, Theorems Well-attested Interior Extremum Theorem, Theorems Well-attested Invariance of Domain, Theorems Well-attested Isoperimetric Inequality, Theorems Well-attested Japanese Theorem for Cyclic Polygons, Theorems Well-attested Jordan Curve Theorem, Theorems Well-attested Kamp's Theorem, Theorems Well-attested Kawasaki's Theorem, Theorems Well-attested Kostant's Convexity Theorem, Theorems Well-attested Kramers' Theorem, Theorems Well-attested Krein-Milman Theorem, Theorems Well-attested Kronecker's Approximation Theorem, Theorems Well-attested Kronecker-Weber Theorem, Theorems Well-attested Kruskal-Katona Theorem, Theorems Well-attested Kruskal's Tree Theorem, Theorems Well-attested Kuhn's Theorem, Theorems Well-attested Kuiper's Theorem, Theorems Well-attested Kuratowski's Theorem, Theorems Well-attested Lafforgue's Theorem, Theorems Well-attested Lagrange's Theorem (Group Theory), Theorems Well-attested Lambek-Moser Theorem, Theorems Well-attested Law of Large Numbers, Theorems Well-attested Law of Quadratic Reciprocity, Theorems Well-attested Lebesgue Differentiation Theorem, Theorems Well-attested Legendre's Three-Square Theorem, Theorems Well-attested Leray-Hirsch Theorem, Theorems Well-attested Lerner Symmetry Theorem, Theorems Well-attested Levy's Continuity Theorem, Theorems Well-attested Lindemann-Weierstrass Theorem, Theorems Well-attested Lindström's Theorem, Theorems Well-attested Liouville's Theorem (Complex Analysis), Theorems Well-attested Los's Theorem, Theorems Well-attested Los-Tarski Theorem, Theorems Well-attested Lusin's Theorem, Theorems Well-attested Mahler's Compactness Theorem, Theorems Well-attested Mahler's Theorem, Theorems Well-attested Malus-Dupin Theorem, Theorems Well-attested Marginal Value Theorem, Theorems Well-attested Maschke's Theorem, Theorems Well-attested Matiyasevich's Theorem, Theorems Well-attested Maximum Modulus Principle, Theorems Well-attested Maximum Theorem, Theorems Well-attested Mayer-Vietoris Theorem, Theorems Well-attested Showing 101 to 150 of 262 in Statement Form Of, page 3 of 6.← Previous123456Next →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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