Definition of curvature in English:



  • 1The fact of being curved or the degree to which something is curved.

    ‘spinal curvature’
    ‘the curvature of the earth’
    ‘it has a distinct curvature near the middle’
    • ‘Similar double curvatures were used for concave lenses, and even more complicated corrections for astigmatism.’
    • ‘Spinal curvatures are an example; these are invariably linked to muscular imbalances.’
    • ‘The geometrical analysis yields the principal curvatures and the Gaussian curvature for each cell on the reconstructed meristem surface.’
    • ‘Circles underlying the curvatures of the seating rows do not appear on the building's exterior, since the theater as a rectangular volume was encased in hotel and office space.’
    • ‘This is remarkable, since it also implies that different mechanistic relations have to be co-ordinated differently in order to get similar curvatures.’
    • ‘Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight.’
    • ‘To approximate the geometric flexibility that could be achieved in concrete, the circular steel frame that replaced it had twenty-eight radius points for laying out the plan's different curvatures.’
    • ‘Are there deviations at very strong curvatures, or for that matter very weak curvatures?’
    • ‘In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the surface.’
    • ‘It is the most graceful of birds in flight and its body curvatures and wing span excite all who witness it.’
    • ‘So are you ready to be bedazzled by the Barcelona curves and curvatures?’
    • ‘Previously, the profile was analyzed only from the curvatures at the top of the rise-decay curve to obtain averaged D at one specific time.’
    • ‘Both curvatures can be treated with back braces as long as the patient's body is still growing.’
    • ‘More detailed analysis showed (unpublished results) that the optimum shape of a bent bilayer should be found by minimizing local energy density as a function of two principal curvatures and the energy can be somewhat decreased.’
    • ‘Many examination techniques are used to evaluate patients presenting with spinal curvatures.’
    • ‘It is actually a response to the curvatures in space-time. Objects that appear to be manipulated by a force are just following the natural pathways along those curves.’
    • ‘The curvatures of the electronically controlled seats and backs can be individually adjusted.’
    • ‘There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed.’
    • ‘Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround.’
    • ‘Clinicians should remain alert for large spinal curvatures when examining adolescents.’
    1. 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane.
      • ‘Measuring the degree of curvature in a surface helps determine potential bending stress and material strain.’
      • ‘These repeatabilities were significant, except mean rate of change of curvature in the xy plane.’
      • ‘By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor.’
      • ‘In the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature.’
      • ‘That curved lines as they can be varied in their degrees of curvature as well as in their lengths, begin on that account to be ornamental.’
      • ‘This illustrates around the periphery the effects of vignetting - loss of brightness and focus - and curvature of straight lines, typical of camera obscura images generally.’
      • ‘Gaussian curvature is positive for surfaces like a hemisphere, which are either concave or convex in all the directions.’
      • ‘A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.’
      • ‘It can even handle greater curvatures than conventional blade designs.’
      • ‘Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil.’
      • ‘The curvature of the surface determines the concentration of light in this direction, used to create lighter or darker regions on the target surface.’
      • ‘We have extended previous studies using DOPE / DOPS mixtures, designed to measure the effect of surface charge on monolayer curvature.’
      • ‘As well as being different in size and degree of curvature, they differ in the presence of a constriction at the base of the crown of the tooth in morphotype B but not A.’
      • ‘In fact the work was of such quality that Weingarten received a prize for work on the lines of curvature of a surface in 1857.’
      • ‘As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation.’
      • ‘In these cases, hydrolysis is shown to take place at the hole edges where the surface curvature is high, providing an exposed site for hydrolysis.’
      • ‘The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section.’
      • ‘The second and central panel is an abstract passage; here, the tension between flat surface and represented curvature is broken by the mottled dark colouring, to yield a paradoxical depth.’
      • ‘The mobility decrements may be thought of as shape factors characterizing the apparent curvature of a target fragment, as determined by gel electrophoresis.’
      • ‘What he suggested was that Bolyai and Lobachevsky had not really introduced new concepts at all but had described the theory of geodesics on surfaces of negative curvature.’
      bend, turn, loop, curl, twist, hook
      View synonyms
    2. 1.2 A numerical quantity expressing curvature.
      • ‘The curvature field along the stem was computed by a numerical analysis of the central line.’
      • ‘A deeper characterization of a helix is that it is the unique curve in 3-space for which the ratio of curvature to torsion is a constant, a result known as Lancret's Theorem.’
      • ‘Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.’
      • ‘For the unsupponed portion, the mean curvature remains constant.’
      • ‘It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4p.’
      • ‘The value assigned for each cell is the value of Gaussian curvature at the cell centroid.’
      • ‘We wish to compare the modern formula for curvature with Huygens's expression of ratios.’
      • ‘Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature.’
      • ‘The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments.’
      • ‘That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!’
      • ‘He attacked a completely new topic to the one he had studied for his doctoral thesis studying the theory of harmonic functions in spaces of constant curvature.’
      • ‘A line is considered a circle with infinite radius and zero curvature.’
      • ‘He showed that spaces of constant curvature could have several different topological structures.’
      • ‘It is found that the square of the mean curvature averaged over the entire simulation box is enhanced if the strength of the bonds in the elastic network are modulated in response to local changes in the composition field.’
      • ‘Some of his work on physical topics relates to his non-euclidean geometry for he examined how the gravitational potential as given by Newton would have to be modified in a space of negative curvature.’
      • ‘Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces.’
      • ‘Although Germain does not offer a physical or geometric derivation of mean curvature, it remains a key concept in the study of minimal surfaces, not to mention the theory of elasticity.’
      • ‘The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere.’
      • ‘The local curvature could then be computed from the coefficients of this quadratic surface.’
      • ‘Therefore, origami models have constant zero Gauss curvature at each interior vertex.’


Late Middle English: via Old French from Latin curvatura, from curvare (see curve).