afín

Afín is a Spanish adjective and noun with several related uses, spanning language, law, and mathematics. In everyday Spanish, afín means "related by affinity" or "akin," used to express similarity or a close relation between things, ideas, or people. It is common in phrases such as “tus intereses son afines a los míos” or “parecidos afines.” In legal and social contexts, the term appears in expressions like “parientes por afinidad,” referring to relatives by marriage (for example, the family of a spouse), as distinct from consanguíneos, or relatives by blood.

Etymologically, afín derives from Latin affinis, meaning "near, related." In Spanish it is often contrasted with consanguíneo to denote relation through marriage or similarity rather than blood ties.

In mathematics and geometry, afín corresponds to the English term “affine.” An affine transformation maps points by x ↦ Ax + b, preserving straight lines and parallelism and, typically, affine combinations. An “espacio afín” is a mathematical space that generalizes vector spaces by lacking a distinguished origin, focusing on points, directions, and their relationships. Core concepts include affine maps, affine spaces, and the affine group (the set of invertible affine transformations). Affine geometry studies properties invariant under affine transformations, such as collinearity and ratios along parallel lines. An “función afín” is a function of the form f(x) = ax + b in one dimension, or f(x) = Ax + b in higher dimensions, with A invertible in the standard bijective setting.

Overall, afín serves as a flexible term bridging everyday language and formal mathematics, signaling closeness, similarity, or a structural relationship rather than strict identity.