evoluten.adj.
/ˈiːvəl(j)uːt/, /ˈɛvəl(j)uːt/, U.S. /ˈɛvəˌl(j)ut/ A. n.† 2. irregular. = involute n. 2. Obsolete. evolute cog n. a tooth on a cogwheel, the two sides of which follow involutes of the circle formed by the circumference of the wheel, designed so that a constant rate of rotation is maintained throughout the contact of the cogwheel with another.
1. Geometry.† b. The developed surface of a cone or cylinder. Cf. development n. 10b. Obsolete. rare.
a. A curve which is the locus of the centres of curvature of another curve, or the envelope of all its normals (normal n. 1). Contrasted with involute n. 2. radius of the evolute n. now rare each of the lines which are tangents to an evolute and normals with respect to its involute.The names evolute and involute allude to the simplest way of demonstrating the curves: the end of a stretched thread unwound from a fixed point on the evolute will trace one of its involutes.
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the world > relative properties > number > geometry > curve > [noun] > locus
locus1675
evolute1704
place1704
trajectory1795
syntractory1820
focal surface1828
synharmonic1850
syntractrix1852
pedal1862
umbilical focal conic1862
umbilical focal conic1862
stigmatic1863
synchronism1867
synchronous curve1867
Steinerian1873
tac-locus1873
strophoid1880
orthoptic locus1882
strophoidal1908
hypercycle1909
1704 C. Hayes Treat. Fluxions iv. 109 (heading) Of the Properties of the Involute and Evolute (figures so call'd).
1728 E. Chambers Cycl. (at cited word) The Radius of the Evolute..is the Part of the Thread comprized between any Point where it is a Tangent to the Evolute, and the correspondent Point, where it terminates on the new Curve.
1767 Philos. Trans. 1766 (Royal Soc.) 56 122 Let APB represent a section of the earth through its axis PCH; ACB an æquatorial diameter; AD the radius of curvature at the point A; and PH the radius of curvature at the point P; DFH the evolute of the curve AEP [etc.].
1851 Encycl. Americana II. 78/2 He [sc. Bernoulli] calculated the loxodromic and catenary curve, the logarithmic spirals, [and] the evolutes of several curved lines.
1882 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.
1920 J. Hambidge Dynamic Symmetry App. 147 The evolute of a logarithmic spiral is another equal logarithmic spiral having the same asymptotic point.
1972 M. Kline Math. Thought iv. 98 In the case of a parabola, the evolute is the curve called a semicubical parabola.
2003 Amer. Math. Monthly 110 594 In-class activities included a development of the equations of a cycloid and its evolute (which becomes the shape of the upper plates for the isochronous pendulum).
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1793 J. Smeaton Narr. Edystone Lighthouse (ed. 2) §60 (note) The figure thus formed would become a kind of evolute of the surface of the whole building.
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the world > relative properties > number > geometry > curve > [noun] > generated by or related to a point > by revolution
cycloid1661
epicycloid1696
trochoid1704
involute figure or curve1706
roulette1708
evolute1753
epicycle1756
involute1796
hypocycloid1843
hypotrochoid1843
axoid1876
epicyclic1878
astroid1886
1753 H. J. Pancronometer ii. 29 The chain, which, before (as it were) tied her [sc. the moon] to the earth, was stretch'd by a defect in the middle; so that her tangent-direction carried her (in an evolute) to her present orb.
1812 J. Playfair Outl. Nat. Philos. I. 77 One of the curves there proposed [for the teeth of wheels], is the evolute of the circle.
1860 Mercantile Marine Mag. May 140 A wheel, having on its circumference a series of evolute-cogs.
1873 R. W. Raymond Silver & Gold ii. 191 Double-armed cams are in use, constructed after an evolute of a circle.
3. Hinduism. In Sankhya philosophy: a principle of nature or being that derives from another principle of nature or being. Cf. evolvent n. 2.
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1862 F. Hall in tr. N. N. Gore Rational Refut. Hindu Philos. Syst. Pref. p. ix (note) ‘Originant’ might answer, or ‘evolvant’ [for prakṛiti]; and ‘originate’ or ‘evolute’ for vikṛiti.
1926 Philos. Rev. 35 53 It is a well-known Sānkhya doctrine that everything—every evolute—is a result of the conjunction of Purusa and Prakriti.
2002 J. Fowler Perspectives of Reality vi. 172 Perception is an evolute of the ahaṃkāra, suggestive that the pure self-awareness that precedes it in evolution is devoid even of the perceptions we can have in dreams.
B. adj.
1. Geometry. Of a curve: having the form of an evolute (sense A. 1).
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1704 J. Harris Lexicon Technicum I. at Involute Involute and Evolute Figures, in Mathematicks, are such as these.
1730 E. Stone tr. G. F. A. de L'Hospital Method Fluxions 94 The Curve BDF is called the Evolute [Fr. dévelopée] of the Curve AHK, or the Evolute Curve.
1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 453/1 s.v. The values of the absciss and ordinate of the Evolute curve EC.
1828 O. Gregory Hutton's Course Math. (ed. 9) II. 351 Any radius of curvature..is a tangent to the evolute curve at the point F.
1830 Philos. Trans. (Royal Soc.) 120 128 The extremities of the two radii of curvature will always remain in contact, forming together a tangent to the evolute circles crossing the line of the centres.
1944 Math. Gaz. 28 169 The cycloid, epicycloid, involute and evolute curves may be traced.
2000 College Math. Jrnl. 31 401 We now give the graphs of several polynomial curves and their evolute curves, and label the N-ranks of the various regions.
2.
a. Botany, Architecture, etc. Turned or curving outward; rolled outward at the edges.
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1800 J. Hull Elements Bot. I. 160 The name of Cotyledon..is preferable, as not implying any certain and definite figure of the parts, and as suiting equally well the involute and evolute cotyledons.
1832 J. Lindley Introd. Bot. i. ii. 190 Exorhizæ evolute, or fully developed.
1866 J. F. Meline Let. 10 Aug. in Two Thousand Miles (1867) xxviii. 232 They still possess and use the elements of decorative art, as applied to pottery, precisely as we find them among the ancient Greeks and Egyptians, the lines straight or spiral, waving, inverted, arched, involute, or evolute.
1951 Jrnl. Hellenic Stud. 71 20 Each evidently finished at the top in a pair of evolute spirals resembling an Aeolic capital.
1959 Bryologist 62 190 Ending in a lateral, downward-curved, tubular, cucullate beak, rarely evolute except on fruiting branches.
b. Zoology. Designating a spiral shell (esp. of an ammonoid or a foraminiferan) which is partly or wholly uncoiled; of or relating to such a shell.
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the world > animals > invertebrates > subkingdom Metazoa > grade Triploblastica or Coelomata > phylum Mollusca > [adjective] > of parts of molluscs > of shell or parts of shell
testaceous1668
trivalvous1681
articulate1685
tabulous1734
concamerated1747
costated1751
ribbed1752
multivalve1753
umbilical1755
multivalved1759
trichite1765
right-handed1776
ventricose1777
unequivalved1788
sinistral1803
white-lipped1813
white-mouthed1815
turriculated1822
umbonial1824
turreted1826
siphunculated1828
columellar1829
sinistrorsal1830
canaliferous1834
spirivalve1835
turrited1835
versant1839
mitriform1843
paucispiral1843
turriculate1843
siphuncled1847
ventricous1850
camerated1851
convolute1851
perforated1851
parietal1854
septiferous1854
planorbiform1856
planorboid1856
trivalved1856
turrite1856
siphunculate1875
turriform1875
umbonic1877
costate1881
interlocular1888
varicated1891
lirate1894
evolute1896
1896 Proc. Amer. Philos. Soc. 35 257 The adult whorl is very evolute, embracing not more than a third of the preceding one.
1961 J. Stubblefield Davies's Introd. Palaeontol. (ed. 3) iv. 116 If we are dealing with an evolute shell there remains only a median internal lobe (also called dorsal or anti-siphonal).
1993 E. N. K. Clarkson Invertebr. Palaeontol. & Evol. (ed. 3) viii. 231/1 Most Nautilida, except for some late Palaeozoic cyrtocones, have coiled shells which may be involute or evolute.
This entry has been updated (OED Third Edition, June 2008; most recently modified version published online June 2022).
evolutev.
/ˈiːvəl(j)uːt/, /ˈɛvəl(j)uːt/, U.S. /ˈɛvəˌl(j)ut/ 1. transitive. Military. To cause to perform an evolution (evolution n. 1). Also intransitive: to perform an evolution. Now rare.
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1735 J. Gittins Compl. Syst. Mil. Discipline 224 If you carefully observe the foregoing Produces and Reduces, you may be able to evolute any Number of Men into what Battle you please.
1757 Word in Time to Both Houses Parl. 9 To teach a large Body of Men to adhere in such a Manner as to bear being evoluted, without disuniting into various Shapes, Aspects, and Situations.
1775 H. Barry Strictures on Friendly Addr. Examined 4 You shall.., like the English troops at Fontenoy, evolute in the face of a victorious and superior army.
1875 Galaxy Feb. 256/2 ‘To evolute’ expresses the action clearly and simply... May I evolute a fleet?
1938 W. C. Shipley Tales Sonoma County (1965) 95 At Fourth of July parades and other outstanding events the Yellow Jackets..would participate, evolute, and go through the manual of arms for the saber.
2. transitive and intransitive. To unfold, to unroll, to open out; to curve outwards. Cf. evolve v. 2. rare.
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the world > space > extension in space > extend in space [verb (intransitive)] > unfurl or unfold
unfoldc1350
unlapa1400
unroll1594
evolute1793
unfurl1814
unwrapc1888
1793 W. Rowley Rational Pract. Physic IV. 410 The causes which accelerate the growth of the embryo and infant, are:..2. The vessels of many parts not being as yet evoluted or expanded to their utmost limits.
1848 M. Edgeworth Orlandino 29 Rolling and winding, convoluting and evoluting.
1996 Afr. Arts 29 72/2 Characterized by dynamic, spiraling glyphic images often evoluting, involuting, and then convoluting in clusters.
3. Originally U.S.
a. intransitive. To evolve, to develop by evolution.
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the world > existence and causation > causation > source or origin > originate, derive, or arise [verb (intransitive)] > arise gradually, develop, or evolve
to grow upa1599
spread1642
develop1744
evolve1851
evolute1872
1872 Appletons' Jrnl. 8 June 633/3 All things, even advertisements, evolute (allow me the term) by slow and uniform degrees.
1884 Cambridge (Mass.) Tribune 15 Aug. If those miserable vagrants could only evolute into respectable people there would be converts to evolution at once.
1907 Daily Chron. 21 Oct. 4/4 This movement, which started so promisingly, and ought by now to have evoluted into honourable well-paid work.
1926 W. J. Locke Old Bridge iv. xv You must let me evolute my own way, carissima.
1966 New Statesman 22 Apr. 575/3 Teenagers who had evoluted in their own style like the fauna of Australia.
1999 A. A. Bebler Challenge of NATO Enlargement 84 Ukraine's position on the process of NATO enlargement further evoluted from ‘not against’ to viewing it as a ‘completely natural and logically motivated process’.
b. transitive. To cause to evolve or develop. O.E.D. Suppl. (1933) labels this sense ‘Journalese’.
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the world > existence and causation > creation > [verb (transitive)] > evolve or develop
unplight?c1400
develop1752
evolve1805
to bring up1823
evolute1874
the world > life > biology > biological processes > evolution > evolve [verb (transitive)]
evolve1805
develop1853
evolute1874
1874 Steubenville (Ohio) Daily Herald & News 28 Nov. 1/3 Now these are the generation of the higher vertebrata in the cosmic period that the Unknowable evoluted the bipedal mammalia.
1885 Rep. Indian Affairs (U.S.) 33 The changed mode of life..will eventually ‘evolute’ ‘Poor Lo’ to a higher sphere.
1896 Daily 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.
1930 Publishers' Weekly 4 Jan. Many more individual factors which are evoluted from knowledge gained by years of experience as well as teaching.
1970 Charleston (W. Va.) Daily Mail 8 Aug. 7/4 (heading) Evoluting the language .
2000 Where we're going Repost in alt.clearing.technology (Usenet newsgroup) 7 Sept. What's important is to ‘evolute’ the world to a more peaceful place.
This entry has been updated (OED Third Edition, June 2008; most recently modified version published online March 2022).
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n.adj.1704v.1735