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If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be "congruent ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

A congruence that has a solution.

The five of Hilbert's axioms which concern geometric equivalence.

A transformation of the form g=D^(T)etaD, where det(D)!=0 and det(D) is the determinant. Isometries are also called congruence transformations.

Two geometric figures are said to exhibit geometric congruence (or "be geometrically congruent") iff one can be transformed into the other by an isometry (Coxeter and ...