Definition of curvature in English:

curvature

noun ˈkəːvətʃə

mass noun

1The fact of being curved or the degree to which something is curved.
弯曲；弯曲度
spinal curvature
脊柱弯曲。
the curvature of the earth
地球曲率。
Example sentencesExamples
- The curvatures of the electronically controlled seats and backs can be individually adjusted.
- Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight.
- It is the most graceful of birds in flight and its body curvatures and wing span excite all who witness it.
- 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.
- This is remarkable, since it also implies that different mechanistic relations have to be co-ordinated differently in order to get similar curvatures.
- Similar double curvatures were used for concave lenses, and even more complicated corrections for astigmatism.
- More detailed analysis showed (unpublished results) that the optimum shape of a bent bilayer should be found by minimizing local energy density as a function of two principal curvatures and the energy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.
- 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.
- The geometrical analysis yields the principal curvatures and the Gaussian curvature for each cell on the reconstructed meristem surface.
- So are you ready to be bedazzled by the Barcelona curves and curvatures?
- 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.
- Both curvatures can be treated with back braces as long as the patient's body is still growing.
- Many examination techniques are used to evaluate patients presenting with spinal curvatures.
- Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround.
- Spinal curvatures are an example; these are invariably linked to muscular imbalances.
- Are there deviations at very strong curvatures, or for that matter very weak curvatures?
- There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed.
- In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the surface.
- Clinicians should remain alert for large spinal curvatures when examining adolescents.
- 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.
1. 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane.
  〔几何〕曲率，（曲线或弧形面）曲度
  Example sentencesExamples
  Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil.
  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.
  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.
  The mobility decrements may be thought of as shape factors characterizing the apparent curvature of a target fragment, as determined by gel electrophoresis.
  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.
  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.
  A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.
  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.
  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 the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature.
  It can even handle greater curvatures than conventional blade designs.
  By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor.
  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.
  The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section.
  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.
  We have extended previous studies using DOPE / DOPS mixtures, designed to measure the effect of surface charge on monolayer curvature.
  As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation.
  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.
  Measuring the degree of curvature in a surface helps determine potential bending stress and material strain.
  Synonyms
  bend, turn, loop, curl, twist, hook
2. 1.2 A numerical quantity expressing curvature.
  曲率
  Example sentencesExamples
  The value assigned for each cell is the value of Gaussian curvature at the cell centroid.
  The local curvature could then be computed from the coefficients of this quadratic surface.
  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 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.
  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 enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments.
  Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.
  Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces.
  We wish to compare the modern formula for curvature with Huygens's expression of ratios.
  Therefore, origami models have constant zero Gauss curvature at each interior vertex.
  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.
  He showed that spaces of constant curvature could have several different topological structures.
  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.
  A line is considered a circle with infinite radius and zero curvature.
  Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature.
  The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere.
  That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!
  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.

Origin

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

Definition of curvature in US English:

curvature

noun

1The fact of being curved or the degree to which something is curved.
弯曲；弯曲度
spinal curvature
脊柱弯曲。
the curvature of the earth
地球曲率。
it has a distinct curvature near the middle
中间部分有明显的弯曲。
Example sentencesExamples
- 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.
- 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.
- Clinicians should remain alert for large spinal curvatures when examining adolescents.
- 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.
- 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.
- 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.
- In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the surface.
- Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight.
- 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.
- There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed.
- 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.
- 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?
- Are there deviations at very strong curvatures, or for that matter very weak curvatures?
- Many examination techniques are used to evaluate patients presenting with spinal curvatures.
- The curvatures of the electronically controlled seats and backs can be individually adjusted.
- Both curvatures can be treated with back braces as long as the patient's body is still growing.
- Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround.
1. 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane.
  〔几何〕曲率，（曲线或弧形面）曲度
  Example sentencesExamples
  Gaussian curvature is positive for surfaces like a hemisphere, which are either concave or convex in all the directions.
  Measuring the degree of curvature in a surface helps determine potential bending stress and material strain.
  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.
  These repeatabilities were significant, except mean rate of change of curvature in the xy plane.
  The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section.
  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.
  In the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature.
  As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation.
  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.
  Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil.
  It can even handle greater curvatures than conventional blade designs.
  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.
  By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor.
  The curvature of the surface determines the concentration of light in this direction, used to create lighter or darker regions on the target surface.
  The mobility decrements may be thought of as shape factors characterizing the apparent curvature of a target fragment, as determined by gel electrophoresis.
  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.
  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.
  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.
  Synonyms
  bend, turn, loop, curl, twist, hook
2. 1.2 A numerical quantity expressing curvature.
  曲率
  Example sentencesExamples
  The local curvature could then be computed from the coefficients of this quadratic surface.
  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.
  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.
  The curvature field along the stem was computed by a numerical analysis of the central line.
  It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4p.
  For the unsupponed portion, the mean curvature remains constant.
  The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere.
  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.
  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.
  Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature.
  He showed that spaces of constant curvature could have several different topological structures.
  We wish to compare the modern formula for curvature with Huygens's expression of ratios.
  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.
  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.
  Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.
  Therefore, origami models have constant zero Gauss curvature at each interior vertex.
  That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!
  Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces.
  The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments.

Origin

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

词汇	curvature
释义	Definition of curvature in English: curvature noun ˈkəːvətʃə mass noun 1The fact of being curved or the degree to which something is curved. 弯曲；弯曲度 spinal curvature 脊柱弯曲。 the curvature of the earth 地球曲率。 Example sentencesExamples The curvatures of the electronically controlled seats and backs can be individually adjusted. Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight. It is the most graceful of birds in flight and its body curvatures and wing span excite all who witness it. 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. This is remarkable, since it also implies that different mechanistic relations have to be co-ordinated differently in order to get similar curvatures. Similar double curvatures were used for concave lenses, and even more complicated corrections for astigmatism. 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. 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. The geometrical analysis yields the principal curvatures and the Gaussian curvature for each cell on the reconstructed meristem surface. So are you ready to be bedazzled by the Barcelona curves and curvatures? 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. Both curvatures can be treated with back braces as long as the patient's body is still growing. Many examination techniques are used to evaluate patients presenting with spinal curvatures. Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround. Spinal curvatures are an example; these are invariably linked to muscular imbalances. Are there deviations at very strong curvatures, or for that matter very weak curvatures? There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed. In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the surface. Clinicians should remain alert for large spinal curvatures when examining adolescents. 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. 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane. 〔几何〕曲率，（曲线或弧形面）曲度 Example sentencesExamples Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil. 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. 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. The mobility decrements may be thought of as shape factors characterizing the apparent curvature of a target fragment, as determined by gel electrophoresis. 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. 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. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem. 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. 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 the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature. It can even handle greater curvatures than conventional blade designs. By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor. 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. The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section. 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. We have extended previous studies using DOPE / DOPS mixtures, designed to measure the effect of surface charge on monolayer curvature. As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation. 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. Measuring the degree of curvature in a surface helps determine potential bending stress and material strain. Synonyms bend, turn, loop, curl, twist, hook 1.2 A numerical quantity expressing curvature. 曲率 Example sentencesExamples The value assigned for each cell is the value of Gaussian curvature at the cell centroid. The local curvature could then be computed from the coefficients of this quadratic surface. 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 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. 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 enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis. Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces. We wish to compare the modern formula for curvature with Huygens's expression of ratios. Therefore, origami models have constant zero Gauss curvature at each interior vertex. 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. He showed that spaces of constant curvature could have several different topological structures. 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. A line is considered a circle with infinite radius and zero curvature. Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature. The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere. That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components! 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. Origin Late Middle English: via Old French from Latin curvatura, from curvare (see curve). Definition of curvature in US English: curvature noun 1The fact of being curved or the degree to which something is curved. 弯曲；弯曲度 spinal curvature 脊柱弯曲。 the curvature of the earth 地球曲率。 it has a distinct curvature near the middle 中间部分有明显的弯曲。 Example sentencesExamples 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. 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. Clinicians should remain alert for large spinal curvatures when examining adolescents. 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. 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. 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. In the 1950s, doubly curved crystal fabrication progressed to include crystals featuring different surface curvatures along orthogonal axes parallel to the surface. Cohen is right that sensible societies shouldn't trust generals to navigate the myriad curvatures of war without civilian oversight. 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. There is, of course, no change to the on-axis response since no lens curvatures or thicknesses were changed. 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. 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? Are there deviations at very strong curvatures, or for that matter very weak curvatures? Many examination techniques are used to evaluate patients presenting with spinal curvatures. The curvatures of the electronically controlled seats and backs can be individually adjusted. Both curvatures can be treated with back braces as long as the patient's body is still growing. Line tensions and director fields depend on the elastic moduli and the spontaneous curvatures of the raft and the surround. 1.1Geometry The degree to which a curve deviates from a straight line, or a curved surface deviates from a plane. 〔几何〕曲率，（曲线或弧形面）曲度 Example sentencesExamples Gaussian curvature is positive for surfaces like a hemisphere, which are either concave or convex in all the directions. Measuring the degree of curvature in a surface helps determine potential bending stress and material strain. 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. These repeatabilities were significant, except mean rate of change of curvature in the xy plane. The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section. 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. In the case of small unilamellar vesicles the enzyme shows sensitivity to different degrees of curvature. As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation. 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. Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil. It can even handle greater curvatures than conventional blade designs. 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. By using different drill diameters, he produced drop lenses of various curvatures in order to vary the magnification factor. The curvature of the surface determines the concentration of light in this direction, used to create lighter or darker regions on the target surface. The mobility decrements may be thought of as shape factors characterizing the apparent curvature of a target fragment, as determined by gel electrophoresis. 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. 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. 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. Synonyms bend, turn, loop, curl, twist, hook 1.2 A numerical quantity expressing curvature. 曲率 Example sentencesExamples The local curvature could then be computed from the coefficients of this quadratic surface. 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. 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. The curvature field along the stem was computed by a numerical analysis of the central line. It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4p. For the unsupponed portion, the mean curvature remains constant. The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere. 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. 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. Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature. He showed that spaces of constant curvature could have several different topological structures. We wish to compare the modern formula for curvature with Huygens's expression of ratios. 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. 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. Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis. Therefore, origami models have constant zero Gauss curvature at each interior vertex. That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components! Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces. The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Origin Late Middle English: via Old French from Latin curvatura, from curvare (see curve).
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