affine
UK[əˈfaɪn]US[əˈfaɪn]
adj
(in mathematics) allowing for or involving transformations which preserve straight lines and the ratios of distances between points lying on a straight line.
adj
(anthropology) related by marriage.
Morpheme Breakdown
af
fine
af
to, toward
fine
end, limit, boundary
Etymology
the word 'affine' entered english in the 15th century from the latin 'affinis', meaning 'bordering on, related by marriage'. 'affinis' itself is a compound of the prefix 'ad-' (to, toward) and 'finis' (end, boundary). the literal sense of 'bordering on' or 'adjacent to' evolved into two abstract meanings. in anthropology, it came to denote a relationship established by marriage, as opposed to blood, metaphorically extending the idea of being brought near or connected. in mathematics, it was adopted in the 18th century to describe geometric transformations that preserve parallelism and ratios along lines, conceptually related to the idea of mapping points to others within a defined, bounded system.
Analysis
Structure: af + fine
af- (variant of 'ad-', latin prefix meaning 'to, toward'); fine (from latin 'finis', meaning 'end, limit, boundary')
Examples
affine geometry studies properties of geometric figures that remain unchanged under affine transformations.
in many societies, affine relatives, such as in-laws, have specific roles and obligations.
the affine connection on the manifold allows for a generalization of the concept of parallel transport.