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curvature|ˈkɜːvətjʊə(r)|
[ad. L. curvātūra bending, f. curvāre, curvāt- to bend: see -ure.]
1. a. The action of curving or bending; the fact, quality, or manner of being curved; curved form; (with pl.) a particular instance of this.
In Pathol. esp. of the spine, of which there are two sorts, angular curvature or Pott's curvature, and lateral curvature.
1665Hooke Microgr. 236 Attributed to the Curvature of the visual Ray..through so differingly Dense a Medium. 1753Hogarth Anal. Beauty 2 A line..of that peculiar curvature. 1800Med. Jrnl. IV. 271 Pains are not even perceived..in curvatures of the back-bone. 1840R. Liston Elem. Surg. (ed. 2) ii. 547 When curvature commences there is very generally more or less weakness of the limbs. 1875Bennett & Dyer Sachs' Bot. iii. iv. 706 Sudden curvature of growing shoots from a blow or concussion. Ibid. 707 The permanent curvature which remains..or the Curvature of Concussion, is the result of a lengthening of the convex and a simultaneous contraction of the concave side.
b. Geom. The amount or rate of deviation (of a curve) from a straight line, or (of a curved surface) from a plane.
circle of curvature: the circle which osculates a curve at any point, and serves to measure the curvature of the curve at that point. centre of c., radius of c..: the centre and radius of the circle of curvature. chord of c. (see quot. 1875). double curvature: that of a curve which twists so as not to lie in one plane, e.g. the curve of a screw.
1710J. Harris Lex. Techn., 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. 1796Hutton Math. Dict., Curve of a Double Curvature, is such a curve as has not all its parts in the same plane. 1807― Course Math. 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. 1866Chamb. Jrnl. xxviii. 271 The axles of the locomotive are directed towards the centre of curvature of the railway. 1875Todhunter Diff. Calc. xxiv. §320 If a straight line be drawn from any point of a curve in any direction, the portion of this straight line which is intercepted by the circle of curvature at the assumed point is called the chord of curvature. 1879Thomson & Tait Nat. Phil. i. i. v, The direction of motion changes from point to point, and the rate of this change, per unit of length of the curve..is called the curvature.
c. A generalization of the notion of curvature applied to a space or manifold of four (or more) dimensions, first made in the theory of non-Euclidean geometry and further developed by Einstein in the general theory of relativity; the property of not being Euclidean or ‘flat’. So curvature of space-time, etc.
1873W. K. Clifford tr. Riemann in Nature 8 May 36/2 If we assume independence of bodies from position, and therefore ascribe to space constant curvature, it must necessarily be finite provided this curvature has ever so small a positive value. 1910Encycl. Brit. XI. 727/2 Riemann's work contains two fundamental conceptions, that of a manifold and that of the measure of curvature of a continuous manifold. 1916Monthly Notices R. Astr. Soc. LXXVI. 707 The mathematical interpretation of G is the curvature of the four-dimensional system of reference. 1920A. S. Eddington Space Time & Gravit. 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. 1920R. W. Lawson tr. Einstein's Relativity: Special & General Theory 127 Half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (‘curvature’) of space caused by the sun. 1959Spitz & Gaynor Dict. Astron. 399 The curvature of space existing in the vicinity of a massive body, like the sun, affects the course of a ray of light. 1966Taylor & 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. 1971Sci. Amer. May 22/3 A gravitational-radiation detector built on this principle should be capable of measuring the gravitational waves (and hence the curvature of space-time) predicted by relativity theory.
2. concr. A curved portion of anything; a curve.
1603Holland Plutarch's Mor. 1312 The said Sistrum being in the upper part round, the curvature and Absis thereof comprehendeth foure things. 1686Goad Celest. Bodies iii. ii. 409 [It] makes the Lofty Curvature of the Celestial Arch to ring. 1800Med. Jrnl. III. 168 The second curvature of the duodenum was partly torn. 1881J. Russell Haigs 3 A magnificent curvature of the river Tweed.
Hence ˈcurvature v. intr., to curve, bend. ˈcurvatured a., having curvature, curved (rare).
a1810Tannahill Poems (1846) 28 Our tiny hero..Ascends the hair's curvatur'd side. 1812J. J. Henry Camp. agst. Quebec 175 We came to the main passage, which curvatured down the hill. |