Congruence

Congruence is the state achieved by coming together, the state of agreement. The Latin congruō meaning “I meet together, I agree”. As an abstract term, congruence means similarity between objects. Congruence, as opposed to equivalence or approximation, is a relation which implies a kind of equivalence, though not complete equivalence.

Mathematics

• Congruence (geometry), being isometric — roughly, the same size and shape
• In modular arithmetic, having the same remainder when divided by a specified integer
• Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure

• Congruence subgroup, a subgroup defined by congruence conditions on the entries of a matrix group with integer entries
• Ramanujan's congruences, congruences for the partition function, p(n), first discovered by Ramanujan in 1919
• Congruence of squares, in number theory, a congruence commonly used in integer factorization algorithms
• 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 space time, or a bundle of world lines

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

Psychology

• In Carl Rogers personality theory, the compliance between ideal self and actual self. See Incongruence.
• In psychology and NLP (Neuro-linguistic programming), congruence could be defined as rapport within oneself, or internal and external consistency, perceived by others as sincerity or certainty.
• Mood congruence,

in psychiatry, congruence between feeling or emotion, and affect display or the manner in which that emotion is being expressed

in psychology, consistency between a patient's symptoms and their mood or mental disorder

Other

• Congruence bias, a type of cognitive bias, similar to confirmation bias
• 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, or shared, derived character states, in which the distributions of supposed homologies among taxa are compared for consistency.
• Horizontal and vertical congruence, two related principles of grouping
• In HTML, the graphical symbol for congruence ≅ is written as ⑃ (hexadecimal), ≅ (decimal) and ≅ (named entity).

See also

• Congruence principle (disambiguation)
• ≡ (disambiguation)