a. and sb. [ad. L. ēvolūt-us, pa. pple. of ēvolvĕre to roll out: see EVOLVE.]
A. adj.
a. Evolute curve = B. 1. b. (See quot. 1835.)
1796. Hutton, Math. Dict., I. 453/1 s.v., The values of the absciss and ordinate of the Evolute curve EC. Ibid. (1828), Course Math., II. 351. Any radius of curvature … is a tangent to the evolute curve at the point F.
1835. Lindley, Introd. Bot. (1848), II. 65. Exorhizie evolute, or fully developed.
B. sb.
1. Math. A curve that is the locus of the centers of curvature of another curve (its involute), or the envelope of all its normals. Radius of the Evolute, Imperfect Evolute (see quots. 1751).
The end of a stretched thread unwound from the evolute will trace the involute; hence the names.
1730–6. in Bailey (folio).
1751. Chambers, Cycl., s.v., The radius of the Evolute is the part of the thread comprised between any point where it is a tangent to the evolute, and the correspondent point where it terminates in the new curve. Ibid., Imperfect Evolute … This curve would be a sort of evolute, and would have its radii; but an imperfect evolute, since the radii are not perpendicular to the first curve.
1852. G. Salmon, Higher Plane Curves, 110. If we take a fourth harmonic to the tangent and the lines joining its point of contact to two fixed points, we shall have a line which may be called the quasi-normal, and its envelope will be a quasi-evolute.
1881. W. Spottiswoode, in Nature, No. 624. 571. The phosphorescence takes the form, approximately, of the evolute of an ellipse.
1882. Proctor, in Knowledge, 24 Nov., 423. The evolute of a circle is a point—the circle’s centre. The evolute of a straight line is either of the points at infinity in direction perpendicular to the line.
¶ 2. Erroneously used for INVOLUTE. Also attrib. in evolute-cog, a cog the two sides of which are involutes of circles.
1812–6. Playfair, Nat. Phil. (1819), I. 81. One of the curves there proposed [for the teeth of wheels] is the evolute of the circle.
1860. Merc. Marine Mag., VII. 140. A wheel, having on its circumference a series of evolute-cogs.
3. The developed surface, ‘development,’ of a cone or cylinder. rare.
1793. Smeaton, Edystone L., § 60, note. The figure thus formed would become a kind of evolute of the surface of the whole building.
