Congruence may refer to:
Mathematics
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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, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group (mathematics), group, ring (mathematics), ring, or vector space) that is compatible with the structure in the ...
, 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 operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...
, having the same remainder when divided by a specified integer
**
Ramanujan's congruences
In mathematics, Ramanujan's congruences are the congruences for the partition function ''p''(''n'') discovered by Srinivasa Ramanujan:
:
\begin
p(5k+4) & \equiv 0 \pmod 5, \\
p(7k+5) & \equiv 0 \pmod 7, \\
p(11k+6) & \equiv 0 \pmod .
\end
In p ...
, congruences for the partition function, , first discovered by Ramanujan in 1919
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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
Matrix (: matrices or matrixes) or MATRIX may refer to:
Science and mathematics
* Matrix (mathematics), a rectangular array of numbers, symbols or expressions
* Matrix (logic), part of a formula in prenex normal form
* Matrix (biology), the ...
, 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#Incongruity
*
Mood congruence between feeling or emotion (in psychiatry and psychology)
* Incongruity
theory of humor
See also
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Congruence bias, a type of cognitive bias, similar to confirmation bias
*
Congruence principle (disambiguation)
*
Hatch mark
Hatch marks (also called hash marks or tick marks) are a form of mathematical notation. They are used in three ways as:
* Unit and value marks — as on a ruler or number line
* Congruence notation in geometry — as on a geometric figure
* Gra ...
, geometric notation for congruent line segments
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≅
*
≡ (disambiguation)
*
≃
In topology, two continuous functions from one topological space to another are called homotopic (from and ) if one can be "continuously deformed" into the other, such a deformation being called a homotopy ( ; ) between the two functions. A ...
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