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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’**‘So are you ready to be bedazzled by the Barcelona curves and curvatures?’**‘The curvatures of the electronically controlled seats and backs can be individually adjusted.’**‘It is the most graceful of birds in flight and its body curvatures and wing span excite all who witness it.’**‘Clinicians should remain alert for large spinal curvatures when examining adolescents.’**‘Many examination techniques are used to evaluate patients presenting with spinal curvatures.’**‘Spinal curvatures are an example; these are invariably linked to muscular imbalances.’**‘Similar double curvatures were used for concave lenses, and even more complicated corrections for astigmatism.’**‘This is remarkable, since it also implies that different mechanistic relations have to be co-ordinated differently in order to get similar curvatures.’**‘The geometrical analysis yields the principal curvatures and the Gaussian curvature for each cell on the reconstructed meristem surface.’**‘Are there deviations at very strong curvatures, or for that matter very weak 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.’**‘There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed.’**‘Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight.’**‘Both curvatures can be treated with back braces as long as the patient's body is still growing.’**‘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.’**‘In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the 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.’**‘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.’**‘Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround.’**‘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.’*

- 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane.
*‘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.’**‘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.’**‘Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil.’**‘Measuring the degree of curvature in a surface helps determine potential bending stress and material strain.’**‘As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation.’**‘The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section.’**‘A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.’**‘We have extended previous studies using DOPE / DOPS mixtures, designed to measure the effect of surface charge on monolayer curvature.’**‘The curvature of the surface determines the concentration of light in this direction, used to create lighter or darker regions on the target surface.’**‘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.’**‘Gaussian curvature is positive for surfaces like a hemisphere, which are either concave or convex in all the directions.’**‘These repeatabilities were significant, except mean rate of change of curvature in the xy plane.’**‘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 the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature.’**‘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.’**‘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.’**‘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.’**‘By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor.’**‘It can even handle greater curvatures than conventional blade designs.’*

**bend**, turn, loop, curl, twist, hook - 1.2A numerical quantity expressing curvature.
*‘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.’**‘Therefore, origami models have constant zero Gauss curvature at each interior vertex.’**‘Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.’**‘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.’**‘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.’**‘He showed that spaces of constant curvature could have several different topological structures.’**‘The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments.’**‘Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces.’**‘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.’**‘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.’**‘We wish to compare the modern formula for curvature with Huygens's expression of ratios.’**‘That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!’**‘Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature.’**‘A line is considered a circle with infinite radius and zero curvature.’**‘The value assigned for each cell is the value of Gaussian curvature at the cell centroid.’**‘The curvature field along the stem was computed by a numerical analysis of the central line.’**‘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.’**‘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.’*

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

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