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The 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.
1. Intricate; complex.
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·lutes
To curl inward.
The curve traced by a point as if it were on a taut string being unwound from another curve.
[Latin involūtus, past participle of involvere, to enwrap; see involve.]