Congruence

Congruence may refer to:

Mathematics

• Congruence (geometry), being the same size and shape
• In modular arithmetic, having the same remainder when divided by a specified integer
  • Ramanujan's congruences, congruences for the partition function, 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 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 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

See also

• Congruence bias, a type of cognitive bias, similar to confirmation bias
• Congruence principle (disambiguation)
• Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
• Hatch mark, geometric notation for congruent line segments
• ≅
• ≡ (disambiguation)
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