Involute

Involute, "rolled inwards," a term applied to leaves having their margins rolled in over their upper surfaces, as in the sticky insect-catching leaves of the butterwort, or in those of the violet, or in the case of many petals. In geometry it is a curve derived from another, termed its evolute (q.v.), by what may be called a process of unwinding. Takingthe simplest case, that of a circle as evolute, if we regard a thread as being wound round a circle, the curve traced out by its free extremity when unwound is the involute of the circle. In any other curve there is a corresponding involute, which is definable as that curve which possesses the property that the length of the tangent drawn from any point on it to the original evolute is equal to the length of the evolute between the tangent point and the point of commencement of the involute. The involute of a cycloid is an equal cycloid; that of a circle is the ordinary spiral; that of the catenary is a tractrix.