curvature love

# curvature

## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The act of curving or the state of being curved.
• noun The ratio of the change in the angle of a tangent that moves over a given arc to the length of the arc.
• noun The limit of this ratio as the length of the arc approaches zero.
• noun The reciprocal of the radius of a circle.
• noun Medicine A curving or bending, especially an abnormal one.

### from The Century Dictionary.

• noun 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.
• noun Continuous bending; the essential character of a curve: applied primarily to lines, but also to surfaces. See phrases below.
• noun Any curving or bending; a flexure.
• noun Something which is curved or bent.

### from the GNU version of the Collaborative International Dictionary of English.

• noun 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.
• noun (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.
• noun (Geom.) the deviation of a curve from a circular form.
• noun See under Absolute.
• noun (Geom.) one that expresses the amount of curvature of a curve.
• noun See under Chord.
• noun See Osculating circle of a curve, under Circle.
• noun (Med.) an abnormal curving of the spine, especially in a lateral direction.
• noun the radius of the circle of curvature, or osculatory circle, at any point of a curve.

• noun The shape of something curved.
• noun mathematics The extent to which a subspace is curved within a metric space.
• noun differential geometry The extent to which a Riemannian manifold is intrinsically curved.

• noun the rate of change (at a point) of the angle between a curve and a tangent to the curve
• noun the property possessed by the curving of a line or surface
• noun (medicine) a curving or bending; often abnormal

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

[Middle English, from Latin curvātūra, from curvātus, past participle of curvāre, to bend, from curvus, curved; see sker- in Indo-European roots.]

## Examples

• The curvature of the spine, spoken of in this work as so common, and as the cause of so many diseases among American women, is what is denominated the _lateral curvature_, and is much more dangerous than the other distortion.

A Treatise on Domestic Economy For the Use of Young Ladies at Home and at School Catharine Esther Beecher 1839

• The Weyl curvature is zero on both the future boundary and past boundary, hence the Big Bang is still well-defined in the cyclic model as the unique hypersurface on which the Weyl curvature vanishes.

Archive 2009-05-01 Gordon McCabe 2009

• It is proposed to abolish the jog, and to swing the east curvature from the east side of Yonge Street opposite College Street south-easterly into Carlton Street at a width of. 100 feet, immediately to the west of the prolongation of Victoria Street, to reduce the width to 80 feet and extend it through at an 80-foot width to Jarvis Street.

• To make the notion of curvature pathology more precise, we will use the manifestly physical idea of tidal force.

Singularities and Black Holes Curiel, Erik 2009

• Another common thought, often adverted to in discussion of the two primary notions, is that singular structure, whether in the form of missing points or incomplete paths, must be related to pathological behavior of some sort on the part of the singular spacetime's curvature, that is, the fundamental deformation of spacetime that manifests itself as “the gravitational field.”

Singularities and Black Holes Curiel, Erik 2009

• The exterior is as pointy as the market demands, but the arch over the entrance is a nice touch, and the door is cut to match its curvature, which is even nicer.

• As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature".

• As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature".

Conservapedia - Recent changes [en] NotesTH 2010

• As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature".

• As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature".

Conservapedia - Recent changes [en] LoganBertram 2010