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单词 convex
释义

convexadj.n.

Brit. /ˌkɒnˈvɛks/, /ˈkɒnvɛks/, U.S. /ˌkɑnˈvɛks/, /kənˈvɛks/, /ˈkɑnˌvɛks/
Etymology: < Latin convexus vaulted, arched, rounded, apparently an old past participle (= convectus ) of convehĕre to carry or bring together (because in forming an arch the extremities of the surface are brought together): in Latin convexus was sometimes used to include concavus : see B. 1c. By Milton stressed conˈvex, which is not infrequent with later poets.For a possible early use see convers n.
A. adj.
a. Curved like the outside of a circle or sphere; having a curvature that bulges toward the point of observation; the reverse of concave.
ΘΚΠ
the world > space > shape > curvature > curved surface > [adjective] > convex
swellingc1000
gibbousc1400
round?1523
convex?a1560
convexed1578
bias1609
out-bowed1613
outbent1625
full1627
outbowing1657
gibbose1682
rounded1712
bulging1812
pot-bellied1814
balloony1861
bombed1872
bombous1878
?a1560 L. Digges Geom. Pract.: Pantometria (1571) Pref. sig. A ij Manyfolde superficies, playne Conuex and Concaue.
1594 T. Blundeville Exercises iii. i. f. 127v The vpper part of such vault is said to be conuex, and ye inward part concaue.
1613 Bp. J. Hall Holy Panegyrick 14 The conuexe or out-bowed side of a vessell.
1706 London Gaz. No. 4292/3 Letters-Patents for the Convex-Lamps.
1794 R. J. Sulivan View of Nature I. 459 Flint breaks with smooth surfaces, one of which is convex, the other concave.
1853 J. F. W. Herschel Pop. Lect. Sci. (1873) v. §13. 191 The earth's surface is..less convex—that is, flatter—as we approach its poles on all sides from the equator.
1879 A. R. Wallace Australasia ix. 195 Its coast being concave instead of convex, and, therefore less open to the cool sea.
b. esp. of glasses, lenses, mirrors, etc. of this shape used for optical purposes.
ΘΚΠ
the world > physical sensation > sight and vision > optical instruments > lens > [adjective] > types of lenses
convex?a1560
planoconvex1665
concavo-convex1677
convexo-concave1693
strong1732
aplanatic1799
periscopic1803
omphaloptic1819
polyzonal1823
shallow1837
first-order1846
periscopical1846
orthoscopic1853
rectilinear1874
overcorrected1875
sphero-cylindrical1881
wide-aperture1882
afocal1887
apochromatic1887
anastigmatic1890
telecentric1892
photovisual1899
aspherical1922
aspheric1923
multifocal1928
plano1944
demagnifying1959
?a1560 L. Digges Geom. Pract.: Pantometria (1571) i. vi. sig. Ciij v Playne conuese or concaue glasses.
a1679 T. Hobbes Seven Philos. Probl. (1682) iv. 33 How comes the Light of the Sun to burn almost any combustible matter by refraction through a convex glass, and by reflection from a concave?
1728 E. Chambers Cycl. at Convexity A Convex Mirror represents its Images smaller than the Objects.
1822 T. Webster Imison's Elem. Sci. & Art (new ed.) I. 237 When parallel rays..fall upon a double convex lens, they will be refracted.
1833 N. Arnott Elements Physics (ed. 5) II. i. 130 The light is made by a convex glass or lens to converge to one point or focus.
1869 J. Tyndall Notes 9 Lect. on Light §104. 16 All the foci, and all the images of a convex mirror are virtual.
B. n. [elliptical use of the adjective.]
1.
a. A convex surface or body; a vault, arch, hemisphere, etc. as viewed from without. Obsolete.
ΘΚΠ
the world > space > shape > curvature > curved surface > [noun] > convexity > convex surface or body
convex1626
umbrellac1770
shield1849
1626 F. Bacon Sylua Syluarum §222 Flat against Flat, and Convex against Convex.
1659 T. Pecke Parnassi Puerperium 160 The sublime convex of the Quirine Hils.
1727 D. Defoe Ess. Hist. Apparitions v. 55 He has apparently posted an Army of ministring Spirits..round this Convex, this Globe the Earth.
1796 J. Morse Amer. Universal Geogr. (new ed.) I. 56 A spherical convex nearly as round as the globe itself.
b. The convex part of anything.
ΘΚΠ
the world > space > shape > curvature > curved surface > [noun] > convexity > convex curve or part
convexity1600
convex1680
back1850
outcurve1902
lens1975
1680 J. Moxon Mech. Exercises I. xii. 217 The middle of the Convex of the Hook.
1816 M. Keating Trav. Eur. & Afr. II. 262 Placed on the convex of a piece of timber.
c. By the poets often applied to the vault of the sky or heavens, hell, etc. Cf. Latin convexum, -a.
ΘΚΠ
the world > the universe > sky, heavens > [noun]
roofeOE
welkinc825
heaveneOE
heightOE
heavenOE
liftOE
loftOE
welkin1122
skies?a1289
firmamentc1290
skewa1300
spherea1300
skewsc1320
hemispherec1374
cope of heavenc1380
clouda1400
skya1425
elementc1485
axle-treea1522
scrowc1540
pole1572
horizona1577
vaulta1586
round?1593
the cope1596
pend1599
floor1600
canopy1604
cope1609
expansion1611
concameration1625
convex1627
concave1635
expansum1635
blue1647
the expanse1667
blue blanket1726
empyrean1727
carry1788
span1803
overhead1865
1627 T. May tr. Lucan Pharsalia (1631) ix. 1 And takes Up to the convexe of the sky his flight.
1667 J. Milton Paradise Lost ii. 434 This huge convex of Fire..immures us round Ninefold. View more context for this quotation
1667 J. Milton Paradise Lost vii. 266 In circuit to the uttermost convex Of this great Round. View more context for this quotation
1700 M. Prior Carmen Sæculare 19 Through the large Convex of the Azure Sky.
1715 T. Tickell in Spectator 8 No. 620 15 Nov. 344 Half Heav'n's Convex glitters with the Flame.
2. A convex glass or lens.
ΘΚΠ
the world > physical sensation > sight and vision > optical instruments > lens > [noun] > other lenses
concave1632
globe1653
meniscus1693
hemispherule1696
convex1705
omphaloptic1728
omphalopter1738
crown lens1764
achromatic1785
condenser1798
meniscus lens1820
Fresnel lens1835
bull's-eye1839
Stanhope lens1850
spot lens1860
amplifier1866
achromat1873
projectora1884
aplanat1890
triplet condenser1892
Aldis lens1902
monocentric1922
Schmidt correcting plate1934
coated lens1948
Panavision1955
Schmidt correcting lens1961
re-imaging1962
1705 G. Berkeley Commonplace Bk. in Wks. (1871) IV. 480 Qu. if blind would think things diminish'd by convexes.
1708 J. Philips Cyder (R.) The polish'd glass, whose small convex Enlarges to ten millions of degrees The mite.
3. A card prepared for cheating by being cut slightly convex along two edges.
ΘΚΠ
society > leisure > entertainment > pastimes > game > card game > card-sharping or cheating > [noun] > card or cards
bum-cardc1555
key card1805
concave1825
strippers1843
convex1874
reader1887
stacked deck1964
1874 Hotten's Slang Dict. (rev. ed.) 127 Concaves and convexes, a pack of cards contrived for cheating, by cutting all the cards from the two to the seven concave, and all from the eight to the king convex. Then by cutting the pack breadthwise a convex card is cut, and by cutting it lengthwise a concave is secured.

Compounds

convex-concave adj.
ΘΚΠ
the world > physical sensation > sight and vision > optical instruments > mirror > [adjective]
unfoiled1640
reflex1672
quicksilvered1754
mirrored1820
convex-concave1841
West Coast1957
the world > space > shape > curvature > curved surface > [adjective] > convex > concavo-convex
concavo-convex1677
convexo-concave1693
convex-concave1841
1841 T. Carlyle On Heroes iii. 169 No twisted, poor convex-concave mirror, reflecting all objects with its own convexities and concavities.

Draft additions 1993

Mathematics. Of a plane figure, a solid, a set (of points), etc.: containing the straight line segment joining any two points in the set. Of a function: having a graph which forms the lower boundary of a convex set. Of a linear combination of quantities: having coefficients which are non-negative and which total 1. Also applied to other entities in analogous senses. Cf. concave adj. Additions.
ΘΚΠ
the world > relative properties > number > geometry > [adjective] > geometrical property
acentric1831
orientated1857
convex1858
unicursal1866
oriented1875
dual1910
concave1942
traceless1966
the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to functions
generating1671
exponential1704
discontinuous1803
functional1806
odd1812
periodic1820
syzygetic1850
convex1858
graphometric1865
polycyclic1869
subrational1875
synectic1876
variational1879
polyhedral1881
holomorphic1886
tropical1887
Gudermannian1888
monogeneous1888
monotonous1890
oscillating1893
monotonic1901
monotone1903
orthogonalized1909
schlicht1925
concave1942
deconvolved1974
unate1978
1858 Q. Jrnl. Pure & Appl. Math. 2 340 Every number n answers to a simple polygon of n + 2 sides: that is, a polygon in which no side cuts another side. The simple polygon may be either convex, or with some angles re-entrant.
1905 J. L. W. V. Jensen in Nyt Tidsskrift for Matematik 16 b. 49 (heading) Om konvekse funktioner og uligheder imellem middelværdier.]
1915 Proc. London Math. Soc. 14 269 Log M(r) is a convex function of log r.
1930 Proc. National Acad. Sci. U.S.A. 16 240 (heading) Combinatory topology of convex regions.
1951 E. W. Barankin in J. Neyman Proc. 2nd Berkeley Symp. Math., Statistics & Probability 167 (heading) Conditional expectation and convex functions.
1959 G. James & R. C. James Math. Dict. (ed. 2) 234/2 A convex linear combination of quantities xi(i=1, 2,...,n) is an expression..∑n1λixi, where ∑n1λi = 1 and each λi is a non-negative real number.
1965 Ann. Math. Statistics 36 703 (heading) Peakedness of distributions of convex combinations.
1974 Adby & Dempster Introd. Optimization Methods i. 10 More formally, a function of a single argument is convex if for all x and y and all numbers λ between 0 and 1, fx + (1 - λ)y) ≦ λf(x) + (1 - λ)f(y).
1980 A. J. Jones Game Theory ii. 109 A continuous game is called convex if for each fixed x, 0≦x≦1, P (x, y) is a convex function of y.

Draft additions 1993

Special collocations (in Mathematics):
convex envelope n. = convex hull n.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set
set1857
interval1902
intersection1909
union1912
lattice1933
matroid1935
closure1937
Steiner triple or triplet system1939
recursive set1943
convex hull1951
power set1953
convex envelope1964
Steiner system1966
Julia set1976
Mandelbrot set1984
1964 A. P. Rpbertson & W. Robertson Topological Vector Spaces i. 45 Each xiA is a convex set containing A called the convex envelope of A.
convex hull n. the smallest convex set which contains a given set.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set
set1857
interval1902
intersection1909
union1912
lattice1933
matroid1935
closure1937
Steiner triple or triplet system1939
recursive set1943
convex hull1951
power set1953
convex envelope1964
Steiner system1966
Julia set1976
Mandelbrot set1984
1951 E. W. Barankin in J. Neyman Proc. 2nd Berkeley Symp. Math., Statistics & Probability 168 The convex hull of a set in ℰk is the smallest convex set containing the given set.
1965 Biometrika 52 331 (heading) The convex hull of a random set of points.
convex programming n. any of various procedures for finding the minimum value of a convex function subject to specified constraints.
ΘΚΠ
the world > relative properties > number > algebra > [noun] > expression > method of calculation or analysis
extrapolation1872
functional analysis1876
inversion1880
Fourier analysis1929
formalism1940
linear programming1949
quadratic programming1951
simplex method1951
convex programming1963
deconvolution1967
1963 Austral. Jrnl. Statistics 5 14 (heading) An algorithm for convex programming.
This entry has not yet been fully updated (first published 1893; most recently modified version published online March 2022).

convexv.

Etymology: < convex adj. The stress varies.
rare.
1. intransitive. To bow or bend convexly; to present a convex side to or toward.
ΘΚΠ
the world > space > shape > curvature > curved surface > form curved surface [verb (intransitive)] > curve convexly
round-bow1605
rounda1616
convex1805
1805 Ld. Collingwood in A. Duncan Nelson (1806) 263 It formed a crescent, convexing to leeward.
1816 H. Douglas Ess. Mil. Bridges iv. 114 The island..convexing towards Entzersdorf in a large, regular bend.
2. transitive. To make convex; to bow or bend (anything) outwards.
ΘΚΠ
the world > space > shape > curvature > curved surface > form curved surface [verb (transitive)] > make convex
round1678
convex1864
hump1878
1864 T. Carlyle Hist. Friedrich II of Prussia IV. xv. ix. 136 Must be imperceptibly convexed a little.
This entry has not yet been fully updated (first published 1893; most recently modified version published online September 2018).
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adj.n.?a1560v.1805
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