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2. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...

3. Congruent number - Wikipedia

   en.wikipedia.org/wiki/Congruent_number

   In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. [1][2] A more general definition includes all positive rational numbers with this property. [3] The sequence of (integer) congruent numbers starts with. For example, 5 is a congruent number because it is the area of ...

4. Congruence relation - Wikipedia

   en.wikipedia.org/wiki/Congruence_relation

   Congruence relation. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]

5. Congruum - Wikipedia

   en.wikipedia.org/wiki/Congruum

   Equivalently, the two annuli between the three yellow circles have equal areas, π times the congruum. In number theory, a congruum (plural congrua) is the difference between successive square numbers in an arithmetic progression of three squares. That is, if , , and (for integers , , and ) are three square numbers that are equally spaced apart ...

6. Isometry - Wikipedia

   en.wikipedia.org/wiki/Isometry

   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". If the transformation is from a metric space ...

7. Similarity (geometry) - Wikipedia

   en.wikipedia.org/wiki/Similarity_(geometry)

   Similarity (geometry) In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.