Congruence may refer to:

Mathematics

Congruence (geometry) In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be ...

, 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 In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his bo ...

, having the same remainder when divided by a specified integer **

Ramanujan's congruences In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function ''p''(''n''). The mathematician Srinivasa Ramanujan discovered the congruences : \begin p(5k+4) & \equiv 0 \pmod 5, \\ p(7k+5) & \equiv 0 \pmod 7, ...

, 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 In mathematics, two square matrices ''A'' and ''B'' over a field are called congruent if there exists an invertible matrix ''P'' over the same field such that :''P''T''AP'' = ''B'' where "T" denotes the matrix transpose. Matrix congruence is ...

, 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 *

Zeller's congruence Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calend ...

, an algorithm to calculate the day of the week for any date *

Scissors congruence The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely m ...

, related to Hilbert's third problem

Mineralogy and chemistry

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

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 Incongruent transition, in chemistry, is a mass transition between two phases which involves a change in chemical composition. This is contrasted with congruent transition, for which the composition remains the same. The transition may be that ...

, 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 Mood congruence is the consistency between a person's emotional state with the broader situations and circumstances being experienced by the persons at that time. By contrast, mood incongruence occurs when the individual's reactions or emotional st ...

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 ...

Mathematics

Mineralogy and chemistry

Psychology

See also