| 释义 |
▪ I. evolute, a. and n.|ˈɛvəljuːt|
[ad. L. ēvolūt-us, pa. pple. of ēvolvĕre to roll out: see evolve.]
A. adj.
a. evolute curve = B 1.
b. (See quot. 1835.)
1796Hutton Math. Dict. I. 453/1 s.v., The values of the absciss and ordinate of the Evolute curve EC. 1828― Course Math. II. 351 Any radius of curvature..is a tangent to the evolute curve at the point F. 1835Lindley Introd. Bot. (1848) II. 65 Exorhizie evolute, or fully developed.
B. n.
1. Math. A curve which is the locus of the centres 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.
1730–6in Bailey (folio). 1751Chambers 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. 1852G. 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. 1881W. Spottiswoode in Nature No. 624. 571 The phosphorescence takes the form, approximately, of the evolute of an ellipse. 1882Proctor 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.
1812–6Playfair Nat. Phil. (1819) I. 81 One of the curves there proposed [for the teeth of wheels] is the evolute of the circle. 1860Merc. 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.
1793Smeaton Edystone L. §60 note, The figure thus formed would become a kind of evolute of the surface of the whole building.
▪ II. evolute, v. orig. U.S.|ˈiːvəljuːt|
[Back-formation from evolution.]
1. intr. To develop by evolution; = evolve v. 8.
1884Cambridge (Mass.) Tribune 15 Aug., If those miserable vagrants could only evolute into respectable people there would be converts to evolution at once. 1891Daily News 11 Dec. 6/3 No one had started lower than himself, but now he had evoluted. 1907Daily Chron. 21 Oct. 4/4 This movement, which started so promisingly, and ought by now to have evoluted into honourable well-paid work. 1926W. J. Locke Old Bridge iv. xv, You must let me evolute my own way, carissima. 1966New Statesman 22 Apr. 575/3 Teenagers who had evoluted in their own style like the fauna of Australia.
2. trans. To evolve, develop. Journalese.
1885Rep. Indian Affairs (U.S.) 33 The changed mode of life..will eventually ‘evolute’ ‘Poor Lo’ to a higher sphere. 1896Daily News 29 Feb. 6/2 It was to be an attempt to ‘evolute’ Mr. Tom Hughes's ‘Tom Brown’ in various directions, to glorify him and bring him up to date. 1899Ibid. 28 Dec. 6/2 The book plate of a millionaire who yesterday was a barman..may in the course of a few generations be ‘evoluted’ into a family emblem fit to take rank with the arms of any aristocratic Briton. 1930Publishers' Weekly 4 Jan., Many more individual factors which are evoluted from knowledge gained by years of experience as well as teaching. |