in·vo·lute
(
in
v
ə-l
t
′)
adj.1. Intricate; complex.
2. a. Botany Having the margins rolled inward.
b. Zoology Having whorls that enclose and obscure earlier whorls. Used of a gastropod shell.
intr.v.in·vo·lut·ed,
in·vo·lut·ing,
in·vo·lutesTo curl inward.
n.The curve traced by a point as if it were on a taut string being unwound from another curve.
[Latininvolūtus, past participle ofinvolvere, to enwrap; see INVOLVE.]
invo·lute′lyadv.

involuteThe parametric equations of an involute of a circle are
x = r cos θ + r θ sin θ,
y = r sin θ - r θ cos θ.