1911 Encyclopædia Britannica/Involution

INVOLUTION (Lat. involvere, to roll up), a rolling up or complication. In arithmetic, involution is the operation of raising a quantity to any power; it is the converse of evolution, which is the operation of extracting any root of a quantity (see Arithmetic; Algebra). In geometry, an involution is a one-to-one correspondence between two ranges of points or between two pencils (see Geometry: Projective). The “involute” of a curve may be regarded as the locus of the extremity of a string when it is unwrapped from the curve (see Infinitesimal Calculus).