curvature

Definitions

  • WordNet 3.6
    • n curvature the property possessed by the curving of a line or surface
    • n curvature the rate of change (at a point) of the angle between a curve and a tangent to the curve
    • n curvature (medicine) a curving or bending; often abnormal "curvature of the spine"
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Webster's Revised Unabridged Dictionary
  • Interesting fact: The curvature of the earth is pretty close to eight inches every mile, or 66 feet every hundred miles.
    • Curvature 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. "The elegant curvature of their fronds."
    • Curvature (Math) The amount of degree of bending of a mathematical curve, or the tendency at any point to depart from a tangent drawn to the curve at that point.
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Century Dictionary and Cyclopedia
    • n curvature Continuous bending; the essential character of a curve: applied primarily to lines, but also to surfaces. See phrases below.
    • n curvature Any curving or bending; a flexure.
    • n curvature Something which is curved or bent.
    • n curvature In projective geometry, susceptibility of being cut in two different points by a straight, independently of whether the construct possessing this property has any point at which two straights inclined to one another and lying in this construct might meet. In metric geometry curvature is often used for the measure of curvature or the reciprocal of the radius of curvature.
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Chambers's Twentieth Century Dictionary
    • n Curvature a curving or bending: the continual bending or the amount of bending from a straight line
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Etymology

Webster's Revised Unabridged Dictionary
L. curvatura,. See Curvate
Chambers's Twentieth Century Dictionary
L. curvus, crooked.

Usage

In literature:

He could still see the beautiful curvature of her young bosom as she raised her arm.
"The Goose Man" by Jacob Wassermann
Like a small moon it edged up the distant curvature of the hull.
"The Memory of Mars" by Raymond F. Jones
I could rig up a level, I suppose; work out an approximation of the curvature.
"Two Thousand Miles Below" by Charles Willard Diffin
He could not calculate a curvature to save his life.
"A Captain in the Ranks" by George Cary Eggleston
The natural curvature of both fetus and passages is thus followed and the extraction rendered easier.
"Special Report on Diseases of Cattle" by U.S. Department of Agriculture
So long as they remain distinct and equal, however close to each other, the independent curvature may evidently be retained.
"The Stones of Venice, Volume I (of 3)" by John Ruskin
Observe how severe and subtle the curvatures are in all the leaves from fig.
"The Stones of Venice, Volume III (of 3)" by John Ruskin
The next point of importance in these beds is the curvature, to which, as well as to fracture, they seem to have been subjected.
"Modern Painters, Volume IV (of V)" by John Ruskin
This curvature presses on some vital part, and the action of his heart is uncertain.
"The Mountain Girl" by Payne Erskine
Target has passed critical planetary curvature.
"A Gift For Terra" by Fox B. Holden
The exact equation for this curvature had to be determined.
"Cube Root of Conquest" by Roger Phillips Graham
He discovered that he could put a crack in the curvature of space.
"Beyond The Thunder" by H. B. Hickey
It would be necessary to consider the curvatures of the fluid surface at the edge of attachment.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 3" by Various
We have spoken of the curvature of a ball or sphere; now what is the curvature of a cylinder?
"Soap-Bubbles" by C. V. Boys
Females (bottom) and immature males have a slight curvature to the rear of the mouth.
"Whales, Dolphins, and Porpoises of the Western North Atlantic" by Stephen Leatherwood
This curvature should conform to the curvature of the finished road.
"The Future of Road-making in America" by Archer Butler Hulbert
The curvature of a surface is determined by the differences of concentration on either side.
"The Mechanism of Life" by Stéphane Leduc
Select the pieces of tube for this instrument as free from curvature as possible.
"The Methods of Glass Blowing and of Working Silica in the Oxy-Gas Flame" by W. A. Shenstone
According to its curvature it is either spherical, cylindrical, elliptical, or parabolic.
"Wireless Transmission of Photographs" by Marcus J. Martin
Versed sine of curvature of toes.
"Remarks on some fossil impressions in the sandstone rocks of Connecticut River" by John Collins Warren
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In news:

The Adjusta- Bow model allows customers to alter the roll's curvature to accommodate a variety of web conditions and materials.
EAW JFL210 Compact Constant Curvature Line Array and JFL118 Subwoofer.
The JFL210 Compact Constant Curvature line array and compatible JFL118 subwoofer from EAW combine to provide a turnkey solution for small- to medium-sized applications.
Clinical trials show Xiaflex may reduce penile curvature in Peyronie's disease.
A Spanish entrepreneur wants to give you a glimpse of the black expanse of space and the curvature of the earth from a most unusual vantage point — a balloon.
More than half a million visits are made to doctors' offices each year to evaluate and treat spine curvatures.
Sami Petersen was diagnosed with scoliosis , a curvature of the spine, at age 11.
When Elisabeth Harkins was first told that she was going to have to wear a brace on her back because of scoliosis , a curvature of the spine, the 13-year-old was a little self-conscious.
Breakthrough Treatment for Spine Curvature Offers Hope to Young Patients.
An abnormal curvature of the spine that rarely causes pain.
00 AM on 11/26, issued at 2:39 AM Alma, GA Baxley, GA Blackshear, GA Bristol, GA. Scoliosis (sko-lee-OH-sis) is an abnormal curvature of the spine that's most evident when a child is standing or walking.
Everyone has some curvature to their spine, but a pronounced curve in a child's back may mean scoliosis .
The balloon may go high enough in the Earth's atmosphere to view the planet's curvature.
Einstein discovered that gravity is not a force but a curvature.
President Reagan is "recovering quite well" from surgery to correct a curvature of the fourth finger of the left hand , Marlin Fitzwater, the White House spokesman, said today.
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In science:

The fluctuations about the saddle point can be separated into massive modes with a curvature of order n and Goldstone modes with a curvature of order mn.
Random Matrix Theory and Chiral Symmetry in QCD
This implies to give four points, so the orthogonal to two q-tangent vectors will cross marking the position of the radius of curvature, and giving us the inverse of the curvature when the continuous limit is approached.
It is the ambiguity. (But only three generations)
The scalar curvature is obtained by contracting the Ricci-tensor, which is the trace of the curvature tensor.
On the solutions of the Cartan equation in Metric Affine Gravity
The metric structure of a Regge triangulation is locally Euclidean everywhere except at the vertices σ0 , (the bones ), where the sum of the dihedral angles, θ(σ2 ), of the incident triangles σ2 ’s is in excess (negative curvature) or in defect (positive curvature) with respect to the 2π flatness constraint.
The modular geometry of Random Regge Triangulations
In contrast to this result experimental data for low temperatures show no curvature or opposite curvature .
Simple Lattice-Models of Ion Conduction: Counter Ion Model vs. Random Energy Model
Now it is well-known that harmonic maps E : (M , g) → (N , h) from Riemannian manifolds of non-negative Ricci curvature to manifolds of nonpositive sectional curvature have strong rigidity properties, via the BochnerLichnerowicz formula, ∆|DE |2 = |D2E |2 + hRicg , E ∗ (h)i − X(E ∗Rh )(ei , ej , ej , ei ).
Cheeger-Gromov Theory and Applications to General Relativity
Next, to proceed further, we need to impose a rather strong curvature assumption on the ambient space-time curvature.
Cheeger-Gromov Theory and Applications to General Relativity
The first step is to show that the bound (6.5) on the ambient curvature R, in this rescaling, gives uniform bounds on the intrinsic and extrinsic curvature of the leaves Στ .
Cheeger-Gromov Theory and Applications to General Relativity
Most of the important properties of the limit set in the constant curvature space continue to hold in the variable curvature space .
Quasiconformal Rigidity of Negatively Curved Three Manifolds
In this particular case the curvature is a consequence only of the presence of the torsion part of the affine connection, since the Riemannian part of the curvature –which depends on the metric tensor and on the associated Christoffel symbol – vanishes.
Geometrical description of spin-2 fields
Rµν is the contracted curvature tensor of the riemannian sector of the curvature.
Geometrical description of spin-2 fields
The transformation rules of affine connection, curvature tensor, Recci tensor and curvature scalar are different from those in general relativity.
Problems on Foundations of General Relativity
In this section we also define the curvature of a symmetric space, and discuss triplets of symmetric spaces with positive, zero and negative curvature, all corresponding to the same symmetric subgroup.
Random matrix theory and symmetric spaces
In this section we introduce the curvature tensor and the sectional curvature of a symmetric space, and we extend the family of symmetric spaces to include also flat or Euclidean–type spaces.
Random matrix theory and symmetric spaces
The sectional curvature is equal to the gaussian curvature on a 2–dimensional manifold.
Random matrix theory and symmetric spaces
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