Isometry

In mathematics, an isometry (from the Greek ἴσος, isos, which means equal | called also congruence, or congruent transformation) is a notion that generalizes that of rigid movement of an object or a geometric figure. Formally, it is a function between two metric spaces that preserves distances. An isometry is any geometric transformation defined in the plane or space that preserves the measurable characteristics of a figure, such as the measures of sides, amplitudes of angles, perimeter, area, and volume, unchanged. Equivalently, we can say that an isometry is a geometric transformation that preserves distances: however we choose two distinct points A and B in the plane or space, the distance of A from B is equal to the distance of their images.

Examples of isometries are translations, rotations, and reflections in the plane or space. Generally, isometries retain, in addition to distances, other geometric concepts such as angles, areas, and lengths.

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