Isometriaa

Isometriaa is a nonstandard term that appears in informal mathematical discussions and some educational materials. It is not part of the formal nomenclature used in most textbooks or journals, and its precise definition can vary by author. In several usages, isometriaa denotes a generalized distance-preserving transformation that allows a uniform rescaling of distances, connecting isometry with similarity.

Formally, for metric spaces (X,d) and (Y,d'), an isometriaa is a map f:X→Y for which there exists a constant k>0 such that, for all x,y in X, d'(f(x), f(y)) = k d(x,y). If k=1, f is an isometry; if k≠1, f acts as a similarity transformation that scales all distances by k.

In Euclidean space, such transformations can be realized by composing a standard isometry (translation, rotation, reflection) with a uniform dilation by factor k. They preserve straight lines, map polygons to similar polygons, and preserve angles when k>0, making them shape-similarity maps rather than exact metric-preserving maps.

Because isometriaa is not a standard term, most formal treatments replace it with "isometry" (k=1) or "similarity" (k>0). The term is mainly used in didactic settings to illustrate the relationship between distance preservation and scaling. See also isometry, similarity transformation, metric space, conformal map.