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Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants . 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.
In mathematics, a congruence is an equivalence relation on the integers. The following sections list important or interesting prime-related congruences. The following sections list important or interesting prime-related congruences.
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
Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo m is denoted a ≡ b (mod m). The parentheses mean that (mod m) applies to the entire equation, not just to the right-hand side (here, b).
The lattice Con(A) of all congruence relations on an algebra A is algebraic. John M. Howie described how semigroup theory illustrates congruence relations in universal algebra: In a group a congruence is determined if we know a single congruence class, in particular if we know the normal subgroup which is the class containing the identity.
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. [ a ] The word isometry is derived from the Ancient Greek : ἴσος isos meaning "equal", and μέτρον metron meaning "measure".
A congruence relation is an equivalence relation whose domain is also the underlying set for an algebraic structure, and which respects the additional structure. In general, congruence relations play the role of kernels of homomorphisms, and the
For example, 5 is a congruent number because it is the area of a (20/3, 3/2, 41/6) triangle. Similarly, 6 is a congruent number because it is the area of a (3,4,5) triangle. 3 and 4 are not congruent numbers.