Congruence may refer to:
Mathematics
*
Congruence (geometry), being the same size and shape
* Congruence or
congruence relation
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done wi ...
, 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, , 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 of squares is a congruence commonly used in integer factorization algorithms.
Derivation
Given a positive integer ''n'', Fermat's factorization method relies on finding numbers ''x'' and ''y'' satisfying the equali ...
, 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, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.
Congruences are an important concept in general relativity, and are also important in parts of Riemanni ...
, 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 (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Ofte ...
, in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of space time, or a bundle of world lines
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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 mineralogy and chemistry, the term congruent (or incongruent) may refer to:
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Congruent dissolution: substances dissolve congruently when the composition of the solid and the dissolved solute stoichiometrically match
*
Congruent melting
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. It can be contrasted with incongruent melting. This generally happens in two-component systems. To take ...
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 Carl Rogers' personality theory, the compliance between ideal self and actual self-see
Carl Rogers#Incongruence
*
Mood congruence between feeling or emotion (in psychiatry and psychology)
* Incongruity
theory of humor
There are many theories of humor which attempt to explain what humor is, what social functions it serves, and what would be considered humorous. Among the prevailing types of theories that attempt to account for the existence of humor, there are p ...
See also
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Congruence bias, a type of cognitive bias, similar to confirmation bias
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Congruence principle (disambiguation)
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Hatch mark, geometric notation for congruent line segments
*
≅
An approximation is anything that is intentionally similar but not exactly equal to something else.
Etymology and usage
The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...
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≡ (disambiguation)
The symbol ≡ (triple bar) is used in science and mathematics with several different meanings. It may refer to the following:
Mathematics
* Identity (mathematics), identity of two mathematical expressions
* Logical biconditional, in logic (if ...
*
≃
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as beco ...
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