curvature

curvature
/kerr"veuh cheuhr, -choor'/, n.
1. the act of curving or the state of being curved.
2. a curved condition, often abnormal: curvature of the spine.
3. the degree of curving of a line or surface.
4. Geom.
a. (at a point on a curve) the derivative of the inclination of the tangent with respect to arc length.
b. the absolute value of this derivative.
5. something curved.
[1375-1425; late ME < L curvatura, equiv. to curvat(us) ptp. of curvare to bend, CURVE + -ura -URE. See -ATE1]

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Measure of the rate of change of direction of a curved line or surface at any point.

In general, it is the reciprocal of the radius of the circle or sphere of best fit to the curve or surface at that point. This notion of best fit derives from the principle that only one circle can be drawn though any three points not on the same line. The radius of curvature at the middle point is approximately equal to the radius of that one circle. This calculation becomes more exact the closer the points are. The precise value is found using a limit. Because a straight line can be thought of as an arc of a circle of infinite radius, its curvature is zero.

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 in mathematics, the rate of change of direction of a curve with respect to distance along the curve. At every point on a circle, the curvature is the reciprocal of the radius; for other curves (and straight lines, which can be regarded as circles of infinite radius), the curvature is the reciprocal of the radius of the circle that most closely conforms to the curve at the given point (see figure—>).

 If the curve is a section of a surface (that is, the curve formed by the intersection of a plane with the surface), then the curvature of the surface at any given point can be determined by suitable sectioning planes. The most useful planes are two that both contain the normal (the line perpendicular to the tangent plane) to the surface at the point (see figure—>). One of these planes produces the section with the greatest curvature among all such sections; the other produces that with the least. These two planes define the two so-called principal directions on the surface at the point; these directions lie at right angles to one another. The curvatures in the principal directions are called the principal curvatures of the surface. The mean curvature of the surface at the point is either the sum of the principal curvatures or half that sum (usage varies among authorities). The total (or Gaussian) curvature (see differential geometry: Curvature of surfaces (differential geometry)) is the product of the principal curvatures.
 

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Universalium. 2010.

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Look at other dictionaries:

  • Curvature — Cur va*ture (k?r v? t?r; 135), n. [L. curvatura. See {Curvate}.] 1. The act of curving, or the state of being bent or curved; a curving or bending, normal or abnormal, as of a line or surface from a rectilinear direction; a bend; a curve. Cowper …   The Collaborative International Dictionary of English

  • curvature — [kʉr′və chər] n. [ME < L curvatura < curvare: see CURVE] 1. a curving or being curved 2. a curve; curved part of anything 3. Geom. the rate of deviation of a curve or curved surface from a straight line or plane surface tangent to it 4. Med …   English World dictionary

  • curvature — 1660s, from L. curvatura a bending, from curvatus, pp. of curvare to bend (see CURVE (Cf. curve)). In non Euclidian geometry, from 1873 …   Etymology dictionary

  • curvature — [n] rounded part of thing, usually body part arc, arch, arching, bend, bow, curve, curving, curvity, deflection, flexure, incurvation, round, shape; concepts 754,757 …   New thesaurus

  • curvature — ► NOUN ▪ the fact of being curved or the degree to which something is curved …   English terms dictionary

  • Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

  • Curvature — (Roget s Thesaurus) < N PARAG:Curvature >N GRP: N 1 Sgm: N 1 curvature curvature curvity curvation Sgm: N 1 incurvature incurvature incurvity| Sgm: N 1 incurvation incurvation Sgm: N 1 bend bend Sgm: N 1 flexure …   English dictionary for students

  • curvature — cur|va|ture [ˈkə:vətʃə US ˈkə:rvətʃər] n [U and C] technical [Date: 1400 1500; : Latin; Origin: curvatura, from curvare; CURVE2] the state of being curved, or the degree to which something is curved curvature of ▪ the curvature of the Earth s… …   Dictionary of contemporary English

  • curvature — [[t]kɜ͟ː(r)vətʃə(r)[/t]] N UNCOUNT: oft N of n The curvature of something is its curved shape, especially when this shape is part of the circumference of a circle. [TECHNICAL] ...the curvature of the earth... He suffered from curvature of the… …   English dictionary

  • curvature — A bending or flexure. See angulation. SYN: curvatura. [L. curvatura, fr. curvo, pp. atus, to bend, curve] angular c. a gibbous deformity, i.e., a sharp angulation of the spine, occurring in Pott disease. SYN: Pott c …   Medical dictionary

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