Congruence: Difference between revisions

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{{Wiktionary|congruence|≅}}

As an [[Abstraction|abstract]] term, '''[[congruence]]''' means [[similarity]] between [[object (philosophy)|object]]s.

'''Congruence''' may refer to:

Congruence, as opposed to [[equivalence]] or [[approximation]], is a [[mathematical relation|relation]] which implies a ''kind'' of equivalence, though not complete equivalence.

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==Mathematics==

* [[Congruence (geometry)]], being the same size and shape

* Congruence or [[congruence relation]], in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure

* In [[modular arithmetic]], having the same remainder when divided by a specified integer

**[[Ramanujan's congruences]], congruences for the partition function, {{math|''p''(''n'')}}, first discovered by Ramanujan in 1919

**[[Congruence subgroup]], a subgroup defined by congruence conditions on the entries of a matrix group with integer entries

**[[Congruence of squares]], in number theory, a congruence commonly used in integer factorization algorithms

* [[Matrix congruence]], an equivalence relation between two matrices

* [[Congruence (manifolds)]], in the theory of smooth manifolds, the set of integral curves defined by a nonvanishing vector field defined on the manifold

* [[Congruence (general relativity)]], in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of spacetime or a bundle of world lines

* [[Zeller's congruence]], an algorithm to calculate the day of the week for any date

* [[Scissors congruence]], related to Hilbert's third problem

==Mineralogy and chemistry==

In [[mathematics]], congruence is formally represented by a [[tilde]] over an equal sign <math>(\cong)</math>, whereas [[approximation]] is jointed by the double-tilde <math>(\approx)</math>. In both cases, the single tilde ([[~]]) may sometimes be used as a substitute (which may cause confusion due to its usage in [[logic]] and [[Programming language|computer programming languages]] for representing [[negation]]). Congruence [[modular arithmetic|modulo]] n is usually denoted "≡" (see [[congruence relation]] for an example).

In mineralogy and chemistry, the term congruent (or incongruent) may refer to:

<!-- Congruent redirect to Congruence -->

* [[Solubility#Incongruent_dissolution|Congruent dissolution]]: substances dissolve congruently when the composition of the solid and the dissolved solute stoichiometrically match

* [[Congruent melting]] occurs during melting of a compound when the composition of the liquid that forms is the same as the composition of the solid

* [[Incongruent transition]], in chemistry, is a mass transition between two phases which involves a change in chemical composition

==Psychology==

* In [[arithmetic]], [[algebra]] and [[encryption]], '''congruence''' refers to a [[congruence relation]].

* In Carl Rogers' personality theory, the compliance between ideal self and actual self-see [[Carl Rogers#Incongruity]]

* In euclidean [[geometry]], '''congruence''' refers to the equivalence of shapes. See [[congruence (geometry)]].

* [[Mood congruence]] between feeling or emotion (in psychiatry and psychology)

* In the theory of [[smooth manifold]]s, especially in the context of [[general relativity]], [[Congruence (general relativity)]] refers to the [[integral curve]]s defined by a [[vector field]].

* Incongruity [[theory of humor]]

* In [[psychology]] and [[Neuro-linguistic programming|NLP]], congruence could be defined as [[rapport]] within [[self (psychology)|oneself]], or internal and external consistency, perceived by others as [[sincerity]] or [[certainty]].

* An alternative definition of congruence in the work of [[Virginia Satir]], one of the sources of [[NLP]], is the balance between self, other and context.

* In [[cladistics]], '''congruence''' is a test of [[homology (biology)|homology]], or shared, derived character states, in which the distributions of supposed homologies among taxa are compared for consistency.

== See also ==

{{disambig}}

* [[Congruence bias]], a type of cognitive bias, similar to confirmation bias

* [[Congruence principle (disambiguation)]]

* [[Hatch mark]], geometric notation for congruent line segments

* [[≅]]

* [[≡ (disambiguation)]]

* [[≃]]

{{disambiguation}}

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