In geometry, a line or curve whose motion creates a surface; something that generates or produces.
From Latin 'generatrix' (she who generates), feminine form of 'generator', from 'generare' (to beget, produce). The term was borrowed directly into English mathematical terminology in the 17th-18th centuries.
A circle rotated around an axis becomes a sphere through its generatrix—this ancient geometric concept inspired modern 3D computer graphics, where generatrices are the invisible skeleton creating every digital shape.
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