curvaturen.

Brit.

/ˈkəːvətʃ(ʊ)ə/,

/ˈkəːvətjʊə/, U.S.

/ˈkərvətʃʊ(ə)r/,

/ˈkərvətʃər/

Forms: late Middle English 1600s curuature, 1600s– curvature.

Origin: A borrowing from Latin. Etymon: Latin curvātūra.

Etymology: < classical Latin curvātūra curved shape or outline, curve, bend, curved part < curvāt- , past participial stem of curvāre curve v. + -ūra -ure suffix¹.Compare Middle French curvature (a1544), and also Middle French corveure, Middle French, French courbure quality or instance of being curved (15th cent.).

1. concrete. A curved portion of anything; a curve.

ΘΚΠ

the world > space > shape > curvature > [noun] > a curve

bightOE

crookingc1380

curvature?a1425

bought1519

compass1545

ply1575

reflexure1578

curve1596

circumflex1601

curb1601

flexion1607

flexure1608

round1608

sinus1615

return1626

inflection1658

curvity1705

sweep1715

tarve1848

?a1425 tr. Guy de Chauliac Grande Chirurgie (N.Y. Acad. Med.) f. 14 (MED) Þe curuature i. bowing [L. curuatura] of þe cubite i. elbowe.

tr. Palladius De re Rustica (Duke Humfrey) (1896) xii. l. 34 Ek..vch merges curuature [of a vine] Of thre yeer old kit from the roote, is sure.

1603 P. Holland tr. Plutarch Morals 1312 The said Sistrum being in the upper part round, the curvature [Fr. curuature] and Absis thereof comprehendeth foure things.

1686 J. Goad Astro-meteorologica iii. ii. 409 [It] makes the Lofty Curvature of the Celestial Arch to ring.

1784 Syst. Anat. I. i. ii. 197 On the upper and fore part of this curvature a small ridge is seen.

1794 J. Whitaker Course Hannibal over Alps II. ii. 174 He rendered the descent into the hollow easier, by giving it two or three curvatures in its course.

1800 Med. & Physical Jrnl. 3 168 The second curvature of the duodenum was partly torn.

1881 J. Russell Haigs of Bemersyde 3 A magnificent curvature of the river Tweed.

1906 A. H. Gould Technic of Operations upon Intestines & Stomach i. 44 Peptic ulcer of the stomach is most frequently found on the lesser curvature and the posterior wall.

1986 M. Abley Beyond Forget xxxviii. 159 He knew every fence and track, every curvature of the bare hills, as intimately as a body.

2013 M. K. Reynolds Flight of Earls 164 Tiny rivulets of butter streamed down the curvatures of the corn on the cob.

a. The action of curving or bending; the state, quality, manner, or fact of being curved; curved form; (occasionally) an instance of this. Also: the extent to which something is curved.

ΘΚΠ

the world > space > shape > curvature > [noun]

curvation?a1425

curvity?a1425

curvaturea1460

bent1541

bend1597

curvedness1598

flexure1628

incurvation1647

compassedness1652

deflexure1656

flexion1656

curvilinearity1756

deflection1821

wind1825

inflection1837

a1460 Knyghthode & Bataile (Pembr. Cambr. 243) l. 580 (MED) A sengil ege is first to strecch in longe, Withoute bosomynge or curuature.

1665 R. Hooke Micrographia 236 Attributed to the Curvature of the visual Ray..through so differingly Dense a Medium.

1699 E. Tyson Orang-outang 11 The Curvature or Flection of the Arms and Legs in our Pygmie..is just the same as in Man; the Arms bending forwards, and the Legs backwards.

1708 J. James tr. C. Perrault Treat. Five Orders of Columns 64 The Curvature of this Member is sometimes so great, that each Part is almost an entire Semi-circle.

1736 R. Nesbitt Human Osteogeny ii. 118 The clavicle..is so perfectly ossified at birth, that it differs very little from an adult in any thing, except its curvature, which is, I think, generally less.

1753 W. Hogarth Anal. Beauty 2 A line..of that peculiar curvature.

1838 J. Bell Health & Beauty i. 57 The nails are at the same time brittle, and wanting in their graceful curvature and roseate hue.

1875 A. W. Bennett & W. T. T. Dyer tr. J. von Sachs Text-bk. Bot. iii. iv. 706 Sudden curvature of growing shoots from a blow or concussion.

1922 A. W. Porterfield tr. J. Wasserman Goose Man 206 He could still see the beautiful curvature of her young bosom as she raised her arm.

1960 in M. Florkin & H. S. Mason Compar. Biochem. I. vi. 244 In fungi and higher plants..the body is anchored at one end and the response to light is shown by a curvature.

1993 Age (Melbourne) (Nexis) 15 Apr. 3 The Australian foot..appears to have a narrower heel and greater curvature than a European's.

2007 E. Plasker 100 Year Lifestyle iv. viii. 104 Your chairs, mattresses, and bedding..should support the natural curvature of your neck and back.

b. An abnormal or exaggerated curve in the spine; the condition (of the spine or part of the spine) of having such a curve.The three main types of curvature of the spine are kyphosis, lordosis, and scoliosis (see the headwords). angular curvature n. = kyphosis n. at kypho- comb. form . lateral curvature n. = scoliosis n.

ΘΚΠ

the world > health and disease > ill health > deformity > deformities of specific parts > [noun] > curvature of spine

curvity?a1425

lordosis1634

scoliosis1706

curvature1762

transcurvation1822

poker back1890

poker spine1917

1762 S. Ingham tr. G. J. Duverney Dis. Bones 3 This is evident in the Curvature of the Spine, and Formation of Bumps.

1800 Med. & Physical Jrnl. 4 271 Pains are not even perceived..in curvatures of the back-bone.

1840 R. Liston Elem. Surg. (ed. 2) ii. 547 When curvature commences there is very generally more or less weakness of the limbs.

1905 Brit. Med. Jrnl. 28 Oct. 1136/1 Incapacitated by lateral curvature and general debility, and entirely dependent on friends.

1954 Pittsburgh Legal Jrnl. 102 243 The x-rays revealed a rotational curvature of the lower spine, which is mild.

2014 Hutchinson (Kansas) News 21 Jan. 1 The Kingman High school junior had surgery..to straighten her crooked spine caused by scoliosis, which is a sideways curvature of the spine that occurs in kids most often during the growth spurt just before puberty.

3. Geometry.

a. The amount or rate of deviation of a curve from a straight line or of a curved surface from a plane; any of several quantities which measure or mathematically characterize this (frequently with distinguishing word, as mean curvature, Gaussian curvature, etc.).Such a quantity is called intrinsic to the surface if it does not depend on the space in which it lies. Otherwise, it is called extrinsic.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > curvature

crookedness1651

flexure1672

flexion1704

curvature1710

1710 J. Harris Lexicon Technicum II Curvature of a Line, is the peculiar manner of its bending or Flexure, whereby it becomes a Curve of such peculiar Properties..The Curvatures of different Circles are to one another Reciprocally as their Radii.

1765 T. H. Croker et al. Compl. Dict. Arts & Sci. II. at Earth The curvature in the elliptical arch ST..can nowhere sensibly differ from the mean curvature at R.

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. 98 Any surface of uniform positive specific curvature..may be bent to fit a sphere.

1896 Proc. London Math. Soc. 27 295 1/R is the principal curvature of the surface.

1963 Sci. & Society 27 180 The product of the principal curvatures is the total (Gauss) curvature of the surface.

2014 H. Guo Mod. Math. & Applic. in Computer Graphics & Vision viii. 192 If the surface has a zero curvature everywhere, the sum of interior angles of a triangle is always π.

b. The degree or manner in which the geometry of a space or manifold (esp. of three of more dimensions) differs from that of Euclidean space; any of several quantities which measure or mathematically characterize this (frequently with distinguishing word, as Riemann curvature, Ricci curvature, etc.); the property or state of being non-Euclidean.The generalization of the notion of curvature to spaces and manifolds originates in the study of non-Euclidean geometry, especially in the work of German mathematician Bernhard Riemann (1826–66). One of the most well known applications of this is found in Einstein's general theory of relativity, where it provides a mathematical framework for describing the curvature of space-time.

ΘΚΠ

the world > relative properties > number > geometry > geometric space > [noun] > non-Euclidean

hyperspace1867

curvature1873

Riemann space1894

non-Euclidean space1939

1873 Illustr. London News 15 Mar. 255/3 The Professor [sc. W. K. Clifford] described what he considered the nature of things would be on the supposition that the curvature of all space is nearly uniform and positive.

1920 A. S. Eddington Space, Time & Gravitation x. 158 We thus get the idea that space-time may have an essential curvature on a great scale independent of the small hummocks due to recognised matter.

1921 Amer. Jrnl. Math. 43 220 This is recognized as a manifold of constant Riemann curvature.

1966 E. F. Taylor & J. A. Wheeler Spacetime Physics iii. 175 The existence of this curvature destroys the possibility of describing motion with respect to a single ideal Euclidean reference frame that pervades all space.

1986 New Scientist 23 Oct. 55/1 In the notes I provide for students on my course in relativity, the computation of the Ricci curvature from this metric takes four typewritten pages, although the final result is in fact 0.

2013 Proc. Royal Soc. A. 469 2 The underlying space in this case is an infinite-dimensional Kähler manifold with positive (but non-constant) curvature.

Phrases

Geometry. In the names of geometric constructions used to study the curvature of a curve or surface.

radius of curvature n. the radius of a circle of curvature.

ΚΠ

1712 R. Cotes Let. 23 Feb. in I. Newton Corr. (1975) V. 234 In making these rules I take the measure of a degree at any point of the Meridian to be proportionate to ye Radius of the curvature of ye Ellipsis at that point.

1807 C. Hutton Course Math. (ed. 5) II. 320 The radius of a circle which has the same curvature with the curve at any given point, is the radius of curvature at that point.

1908 Proc. Royal Soc. A. 81 392 In the neighbourhood of the vertex of the conic the resistance to bending makes both the principal radii of curvature finite.

2011 Economist 12 Mar. (Technol. Q.) 16/2 These tricks..allow a flexible circuit to be bent with a radius of curvature of less than 0.1 millimetres–in other words, folded like paper–without breaking.

centre of curvature n. the centre of a circle of curvature.

ΚΠ

1736 J. Colson tr. I. Newton Method of Fluxions 60 Therefore the Center of Curvature to any Point of a Curve, is the Center of a Circle equally curved.

1866 Chambers's Jrnl. xxviii. 271 The axles of the locomotive are directed towards the centre of curvature of the railway.

1951 Country Life 2 Nov. 1453/1 If a rainbow is formed when the sun is just rising..it is possible for the arch to be seen as a complete semi-circle... At all other times..something less than a semi-circle is seen because the centre of curvature..is below the horizon.

2016 Amer. Math. Monthly 123 442 The two lines through the two axles of a bicycle's wheels intersect at the center of curvature of the path traced by the rear wheel, regardless of the direction of the front wheel.

circle of curvature n. the circle that touches a curve at a given point so as to have the same tangent at that point and which, of all such circles, offers the closest approximation to the curve; = osculating circle n. at osculating adj. Compounds.

ΚΠ

1742 C. MacLaurin Treat. Fluxions I. xi. 305 This circle is called the circle of curvature, its center the center of curvature, and its semidiameter the ray of curvature, belonging to the point of contact.

1889 J. M. Taylor Elements Differential & Integral Calculus xii. 172 At a point of maximum or minimum curvature, the circle of curvature does not cut the curve.

1980 R. B. Angel Relativity vii. 150 If the curve happens to be turning sharply at the given point then the circle of curvature at that point will be relatively small.

2007 Computer-aided Design 39 126/2 Any circle of curvature of a spiral encloses all smaller circles of curvature and is enclosed by all larger circles of curvature.

chord of curvature n. now rare a line joining a point of a curve and the circumference of the circle of curvature at that point.

ΚΠ

1742 C. MacLaurin Treat. Fluxions II. xii. 478 The rectangle contained by half the chord of curvature and the right line which measures the gravity.

1860 I. Todhunter Treat. Differential Calculus (ed. 3) xxiv. §320 If a line be drawn from any point of a curve in any direction, the portion of this line which is intercepted by the circle of curvature at the assumed point is called the chord of curvature.

1930 Edinb. Math. Notes 26 19 PR, The chord of curvature through P, is parallel to the tangent at Q.

Compounds

curvature tensor n. Mathematics any of several tensors used to describe the curvature (sense 3b) of a space or manifold; esp. the Riemann–Christoffel tensor.

ΚΠ

1921 Amer. Jrnl. Math. 43 213 The curvature-tensor (Riemann-Christoffel-Tensor)..can be written in the form: B_ρμνσ = ¹/ _{n − 2} (g_ρνL_μσ − g_μνL_ρσ − g_ρσL_μν + g_μσL_ρν).

1970 Ann. Math. 91 312 R will denote the curvature tensor determined by g, and K, the corresponding sectional curvature.

2014 P. Renteln Manifolds, Tensors & Forms viii. 206 From the Riemann curvature tensor we can construct various other curvature tensors by contraction.

Derivatives

ˈcurvatured adj. rare having curvature, curved.

ΘΚΠ

the world > space > shape > curvature > [adjective]

crooked?c1225

roundc1300

ybentc1330

bentc1374

cambera1387

curvate?a1425

curve?a1425

curved?a1425

bowingc1440

crumped1480

bowed1483

bended1495

bowlanda1522

compass?1523

curbed?1541

compassed1551

compassing1576

curvated1598

orbed1598

curving1609

ridgill-backed1611

incurved1623

inflected1646

incurvate1647

curvous1661

incurvated1665

swayed1688

bending1697

circumflex1707

curval1730

sweeping1772

bendy1800

curvatureda1810

curvative1846

hooped1852

swept1903

a1810 R. Tannahill Poems & Songs (1815) 13 Our tiny hero..Ascends the hair's curvatur'd side.

1844 Lancet 3 Feb. 605/1 I propose to accomplish my first object by supports applied to the curvatured form.

1970 Music & Lett. 51 301 The lecherous Harris (who used to smuggle pornographic books in from France in a convenient curvatured spine that he regrettably possessed).

This entry has been updated (OED Third Edition, September 2017; most recently modified version published online March 2022).

单词	curvature
释义	curvaturen. Brit. /ˈkəːvətʃ(ʊ)ə/, /ˈkəːvətjʊə/, U.S. /ˈkərvətʃʊ(ə)r/, /ˈkərvətʃər/ Forms: late Middle English 1600s curuature, 1600s– curvature. Origin: A borrowing from Latin. Etymon: Latin curvātūra. Etymology: < classical Latin curvātūra curved shape or outline, curve, bend, curved part < curvāt- , past participial stem of curvāre curve v. + -ūra -ure suffix¹.Compare Middle French curvature (a1544), and also Middle French corveure, Middle French, French courbure quality or instance of being curved (15th cent.). 1. concrete. A curved portion of anything; a curve. ΘΚΠ the world > space > shape > curvature > [noun] > a curve bightOE crookingc1380 curvature?a1425 bought1519 compass1545 ply1575 reflexure1578 curve1596 circumflex1601 curb1601 flexion1607 flexure1608 round1608 sinus1615 return1626 inflection1658 curvity1705 sweep1715 tarve1848 ?a1425 tr. Guy de Chauliac Grande Chirurgie (N.Y. Acad. Med.) f. 14 (MED) Þe curuature i. bowing [L. curuatura] of þe cubite i. elbowe. tr. Palladius De re Rustica (Duke Humfrey) (1896) xii. l. 34 Ek..vch merges curuature [of a vine] Of thre yeer old kit from the roote, is sure. 1603 P. Holland tr. Plutarch Morals 1312 The said Sistrum being in the upper part round, the curvature [Fr. curuature] and Absis thereof comprehendeth foure things. 1686 J. Goad Astro-meteorologica iii. ii. 409 [It] makes the Lofty Curvature of the Celestial Arch to ring. 1784 Syst. Anat. I. i. ii. 197 On the upper and fore part of this curvature a small ridge is seen. 1794 J. Whitaker Course Hannibal over Alps II. ii. 174 He rendered the descent into the hollow easier, by giving it two or three curvatures in its course. 1800 Med. & Physical Jrnl. 3 168 The second curvature of the duodenum was partly torn. 1881 J. Russell Haigs of Bemersyde 3 A magnificent curvature of the river Tweed. 1906 A. H. Gould Technic of Operations upon Intestines & Stomach i. 44 Peptic ulcer of the stomach is most frequently found on the lesser curvature and the posterior wall. 1986 M. Abley Beyond Forget xxxviii. 159 He knew every fence and track, every curvature of the bare hills, as intimately as a body. 2013 M. K. Reynolds Flight of Earls 164 Tiny rivulets of butter streamed down the curvatures of the corn on the cob. 2. a. The action of curving or bending; the state, quality, manner, or fact of being curved; curved form; (occasionally) an instance of this. Also: the extent to which something is curved. ΘΚΠ the world > space > shape > curvature > [noun] curvation?a1425 curvity?a1425 curvaturea1460 bent1541 bend1597 curvedness1598 flexure1628 incurvation1647 compassedness1652 deflexure1656 flexion1656 curvilinearity1756 deflection1821 wind1825 inflection1837 a1460 Knyghthode & Bataile (Pembr. Cambr. 243) l. 580 (MED) A sengil ege is first to strecch in longe, Withoute bosomynge or curuature. 1665 R. Hooke Micrographia 236 Attributed to the Curvature of the visual Ray..through so differingly Dense a Medium. 1699 E. Tyson Orang-outang 11 The Curvature or Flection of the Arms and Legs in our Pygmie..is just the same as in Man; the Arms bending forwards, and the Legs backwards. 1708 J. James tr. C. Perrault Treat. Five Orders of Columns 64 The Curvature of this Member is sometimes so great, that each Part is almost an entire Semi-circle. 1736 R. Nesbitt Human Osteogeny ii. 118 The clavicle..is so perfectly ossified at birth, that it differs very little from an adult in any thing, except its curvature, which is, I think, generally less. 1753 W. Hogarth Anal. Beauty 2 A line..of that peculiar curvature. 1838 J. Bell Health & Beauty i. 57 The nails are at the same time brittle, and wanting in their graceful curvature and roseate hue. 1875 A. W. Bennett & W. T. T. Dyer tr. J. von Sachs Text-bk. Bot. iii. iv. 706 Sudden curvature of growing shoots from a blow or concussion. 1922 A. W. Porterfield tr. J. Wasserman Goose Man 206 He could still see the beautiful curvature of her young bosom as she raised her arm. 1960 in M. Florkin & H. S. Mason Compar. Biochem. I. vi. 244 In fungi and higher plants..the body is anchored at one end and the response to light is shown by a curvature. 1993 Age (Melbourne) (Nexis) 15 Apr. 3 The Australian foot..appears to have a narrower heel and greater curvature than a European's. 2007 E. Plasker 100 Year Lifestyle iv. viii. 104 Your chairs, mattresses, and bedding..should support the natural curvature of your neck and back. b. An abnormal or exaggerated curve in the spine; the condition (of the spine or part of the spine) of having such a curve.The three main types of curvature of the spine are kyphosis, lordosis, and scoliosis (see the headwords). angular curvature n. = kyphosis n. at kypho- comb. form . lateral curvature n. = scoliosis n. ΘΚΠ the world > health and disease > ill health > deformity > deformities of specific parts > [noun] > curvature of spine curvity?a1425 lordosis1634 scoliosis1706 curvature1762 transcurvation1822 poker back1890 poker spine1917 1762 S. Ingham tr. G. J. Duverney Dis. Bones 3 This is evident in the Curvature of the Spine, and Formation of Bumps. 1800 Med. & Physical Jrnl. 4 271 Pains are not even perceived..in curvatures of the back-bone. 1840 R. Liston Elem. Surg. (ed. 2) ii. 547 When curvature commences there is very generally more or less weakness of the limbs. 1905 Brit. Med. Jrnl. 28 Oct. 1136/1 Incapacitated by lateral curvature and general debility, and entirely dependent on friends. 1954 Pittsburgh Legal Jrnl. 102 243 The x-rays revealed a rotational curvature of the lower spine, which is mild. 2014 Hutchinson (Kansas) News 21 Jan. 1 The Kingman High school junior had surgery..to straighten her crooked spine caused by scoliosis, which is a sideways curvature of the spine that occurs in kids most often during the growth spurt just before puberty. 3. Geometry. a. The amount or rate of deviation of a curve from a straight line or of a curved surface from a plane; any of several quantities which measure or mathematically characterize this (frequently with distinguishing word, as mean curvature, Gaussian curvature, etc.).Such a quantity is called intrinsic to the surface if it does not depend on the space in which it lies. Otherwise, it is called extrinsic. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > curvature crookedness1651 flexure1672 flexion1704 curvature1710 1710 J. Harris Lexicon Technicum II Curvature of a Line, is the peculiar manner of its bending or Flexure, whereby it becomes a Curve of such peculiar Properties..The Curvatures of different Circles are to one another Reciprocally as their Radii. 1765 T. H. Croker et al. Compl. Dict. Arts & Sci. II. at Earth The curvature in the elliptical arch ST..can nowhere sensibly differ from the mean curvature at R. 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. 98 Any surface of uniform positive specific curvature..may be bent to fit a sphere. 1896 Proc. London Math. Soc. 27 295 1/R is the principal curvature of the surface. 1963 Sci. & Society 27 180 The product of the principal curvatures is the total (Gauss) curvature of the surface. 2014 H. Guo Mod. Math. & Applic. in Computer Graphics & Vision viii. 192 If the surface has a zero curvature everywhere, the sum of interior angles of a triangle is always π. b. The degree or manner in which the geometry of a space or manifold (esp. of three of more dimensions) differs from that of Euclidean space; any of several quantities which measure or mathematically characterize this (frequently with distinguishing word, as Riemann curvature, Ricci curvature, etc.); the property or state of being non-Euclidean.The generalization of the notion of curvature to spaces and manifolds originates in the study of non-Euclidean geometry, especially in the work of German mathematician Bernhard Riemann (1826–66). One of the most well known applications of this is found in Einstein's general theory of relativity, where it provides a mathematical framework for describing the curvature of space-time. ΘΚΠ the world > relative properties > number > geometry > geometric space > [noun] > non-Euclidean hyperspace1867 curvature1873 Riemann space1894 non-Euclidean space1939 1873 Illustr. London News 15 Mar. 255/3 The Professor [sc. W. K. Clifford] described what he considered the nature of things would be on the supposition that the curvature of all space is nearly uniform and positive. 1920 A. S. Eddington Space, Time & Gravitation x. 158 We thus get the idea that space-time may have an essential curvature on a great scale independent of the small hummocks due to recognised matter. 1921 Amer. Jrnl. Math. 43 220 This is recognized as a manifold of constant Riemann curvature. 1966 E. F. Taylor & J. A. Wheeler Spacetime Physics iii. 175 The existence of this curvature destroys the possibility of describing motion with respect to a single ideal Euclidean reference frame that pervades all space. 1986 New Scientist 23 Oct. 55/1 In the notes I provide for students on my course in relativity, the computation of the Ricci curvature from this metric takes four typewritten pages, although the final result is in fact 0. 2013 Proc. Royal Soc. A. 469 2 The underlying space in this case is an infinite-dimensional Kähler manifold with positive (but non-constant) curvature. Phrases Geometry. In the names of geometric constructions used to study the curvature of a curve or surface. a. radius of curvature n. the radius of a circle of curvature. ΚΠ 1712 R. Cotes Let. 23 Feb. in I. Newton Corr. (1975) V. 234 In making these rules I take the measure of a degree at any point of the Meridian to be proportionate to ye Radius of the curvature of ye Ellipsis at that point. 1807 C. Hutton Course Math. (ed. 5) II. 320 The radius of a circle which has the same curvature with the curve at any given point, is the radius of curvature at that point. 1908 Proc. Royal Soc. A. 81 392 In the neighbourhood of the vertex of the conic the resistance to bending makes both the principal radii of curvature finite. 2011 Economist 12 Mar. (Technol. Q.) 16/2 These tricks..allow a flexible circuit to be bent with a radius of curvature of less than 0.1 millimetres–in other words, folded like paper–without breaking. b. centre of curvature n. the centre of a circle of curvature. ΚΠ 1736 J. Colson tr. I. Newton Method of Fluxions 60 Therefore the Center of Curvature to any Point of a Curve, is the Center of a Circle equally curved. 1866 Chambers's Jrnl. xxviii. 271 The axles of the locomotive are directed towards the centre of curvature of the railway. 1951 Country Life 2 Nov. 1453/1 If a rainbow is formed when the sun is just rising..it is possible for the arch to be seen as a complete semi-circle... At all other times..something less than a semi-circle is seen because the centre of curvature..is below the horizon. 2016 Amer. Math. Monthly 123 442 The two lines through the two axles of a bicycle's wheels intersect at the center of curvature of the path traced by the rear wheel, regardless of the direction of the front wheel. c. circle of curvature n. the circle that touches a curve at a given point so as to have the same tangent at that point and which, of all such circles, offers the closest approximation to the curve; = osculating circle n. at osculating adj. Compounds. ΚΠ 1742 C. MacLaurin Treat. Fluxions I. xi. 305 This circle is called the circle of curvature, its center the center of curvature, and its semidiameter the ray of curvature, belonging to the point of contact. 1889 J. M. Taylor Elements Differential & Integral Calculus xii. 172 At a point of maximum or minimum curvature, the circle of curvature does not cut the curve. 1980 R. B. Angel Relativity vii. 150 If the curve happens to be turning sharply at the given point then the circle of curvature at that point will be relatively small. 2007 Computer-aided Design 39 126/2 Any circle of curvature of a spiral encloses all smaller circles of curvature and is enclosed by all larger circles of curvature. d. chord of curvature n. now rare a line joining a point of a curve and the circumference of the circle of curvature at that point. ΚΠ 1742 C. MacLaurin Treat. Fluxions II. xii. 478 The rectangle contained by half the chord of curvature and the right line which measures the gravity. 1860 I. Todhunter Treat. Differential Calculus (ed. 3) xxiv. §320 If a line be drawn from any point of a curve in any direction, the portion of this line which is intercepted by the circle of curvature at the assumed point is called the chord of curvature. 1930 Edinb. Math. Notes 26 19 PR, The chord of curvature through P, is parallel to the tangent at Q. Compounds curvature tensor n. Mathematics any of several tensors used to describe the curvature (sense 3b) of a space or manifold; esp. the Riemann–Christoffel tensor. ΚΠ 1921 Amer. Jrnl. Math. 43 213 The curvature-tensor (Riemann-Christoffel-Tensor)..can be written in the form: B_ρμνσ = ¹/ _{n − 2} (g_ρνL_μσ − g_μνL_ρσ − g_ρσL_μν + g_μσL_ρν). 1970 Ann. Math. 91 312 R will denote the curvature tensor determined by g, and K, the corresponding sectional curvature. 2014 P. Renteln Manifolds, Tensors & Forms viii. 206 From the Riemann curvature tensor we can construct various other curvature tensors by contraction. Derivatives ˈcurvatured adj. rare having curvature, curved. ΘΚΠ the world > space > shape > curvature > [adjective] crooked?c1225 roundc1300 ybentc1330 bentc1374 cambera1387 curvate?a1425 curve?a1425 curved?a1425 bowingc1440 crumped1480 bowed1483 bended1495 bowlanda1522 compass?1523 curbed?1541 compassed1551 compassing1576 curvated1598 orbed1598 curving1609 ridgill-backed1611 incurved1623 inflected1646 incurvate1647 curvous1661 incurvated1665 swayed1688 bending1697 circumflex1707 curval1730 sweeping1772 bendy1800 curvatureda1810 curvative1846 hooped1852 swept1903 a1810 R. Tannahill Poems & Songs (1815) 13 Our tiny hero..Ascends the hair's curvatur'd side. 1844 Lancet 3 Feb. 605/1 I propose to accomplish my first object by supports applied to the curvatured form. 1970 Music & Lett. 51 301 The lecherous Harris (who used to smuggle pornographic books in from France in a convenient curvatured spine that he regrettably possessed). This entry has been updated (OED Third Edition, September 2017; most recently modified version published online March 2022). curvaturev. Brit. /ˈkəːvətʃ(ʊ)ə/, /ˈkəːvətjʊə/, U.S. /ˈkərvətʃər/, /ˈkərvəˌtʃʊ(ə)r/ Origin: Formed within English, by conversion. Etymon: curvature n. Etymology: < curvature n. rare. intransitive and transitive. To curve, bend. ΘΚΠ the world > space > shape > curvature > be or become curved or bent [verb (intransitive)] beyc888 bowOE fold13.. crumpc1325 windc1374 courbe1377 curb1377 plyc1395 bend1398 ploy?1473 bowl1513 bought1521 tirve1567 crookle1577 crook1579 compass1588 round1613 incurvate1647 circumflex1661 arcuate1678 to round off1678 sweep1725 curve1748 curvaturea1811 the world > space > shape > curvature > curve or bend [verb (transitive)] beyc888 bowa1300 incrooka1340 inbowa1382 crook1382 plya1393 inflectc1425 courbe1430 wryc1450 cralla1475 crumbc1490 bought1521 compass1542 incurvate1578 ploy1578 incurve1610 curve1615 circumflex1649 wheel1656 curb1662 crumpa1821 curvaturec1933 a1811 J. J. Henry Accurate Acct. Campaign against Quebec (1812) 175 We came to the main passage, which curvatured down the hill. 1845 Mother's Mag. Jan. 10 The breath that is shortened, the spine that is curvaturing. c1933 in Brandon (Manitoba) Sun (1977) 7 Oct. 12/3 He..fell into Jigg's silo pit and curvatured his spine. This entry has been updated (OED Third Edition, September 2017; most recently modified version published online March 2022). < n.?a1425v.a1811
随便看	cerulic acid cerulific cerulignol cerulignone cerulous cerumen cerumens ceruminiferous ceruminous ceruminous glands ceruse ceruse of antimony cerused ceruses cerusite cerusites cerussal cerussite cerussites cervanthropy cervantic cervantist cervantite cervelat cervelats

curvaturen.

Phrases

Compounds

Derivatives

curvaturev.