High Quality Content by WIKIPEDIA articles! In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. Equivalently, it is the envelope of the normals to a curve. The original curve is an involute of its evolute.Apollonius (c. 200 BC) discussed evolutes in Book V of his Conics. However, Huygens is sometimes credited with being the first to study them (1673).The radius of curvature at ?(s) is, in magnitude, the radius of the circle which forms the best approximation of the curve to second order at the point: that is, it is the radius of the circle making second order contact with the curve, the osculating circle. The sign of the radius of curvature indicates the direction in which the osculating circle moves if it is parameterized in the same direction as the curve at the point of contact: it is positive if the circle moves in a counterclockwise sense, and negative otherwise.

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