单词 | convex |
释义 | convexadj.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.] 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, f(λx + (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 xi∈A 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. 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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