Congruence

Congruence (symbol: ≅) 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 approximation, is a relation which implies a species of equivalence.

Mathematics

• Congruence (geometry), being isometric — roughly, 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, 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
• 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
• Scissors congruence, related to Hilbert's third problem

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)
• Hatch mark, geometric notation for congruent line segments
• ≅ (disambiguation)
• ≡ (disambiguation)
• ≃