The Collaborative International Dictionary of English v.0.48:

Curvature \Cur"va*ture\ (k?r"v?-t?r; 135), n. [L. curvatura. See
   Curvate.]
   1. 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.
      --Cowper.
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            The elegant curvature of their fronds. --Darwin.
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   2. (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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   Aberrancy of curvature (Geom.), the deviation of a curve
      from a circular form.

   Absolute curvature. See under Absolute.

   Angle of curvature (Geom.), one that expresses the amount
      of curvature of a curve.

   Chord of curvature. See under Chord.

   Circle of curvature. See Osculating circle of a curve,
      under Circle.

   Curvature of the spine (Med.), an abnormal curving of the
      spine, especially in a lateral direction.

   Radius of curvature, the radius of the circle of curvature,
      or osculatory circle, at any point of a curve.
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The Collaborative International Dictionary of English v.0.48:

Circle \Cir"cle\ (s[~e]r"k'l), n. [OE. cercle, F. cercle, fr. L.
   circulus (Whence also AS. circul), dim. of circus circle,
   akin to Gr. kri`kos, ki`rkos, circle, ring. Cf. Circus,
   Circum-.]
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   1. A plane figure, bounded by a single curve line called its
      circumference, every part of which is equally distant from
      a point within it, called the center.
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   2. The line that bounds such a figure; a circumference; a
      ring.
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   3. (Astron.) An instrument of observation, the graduated limb
      of which consists of an entire circle.
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   Note: When it is fixed to a wall in an observatory, it is
         called a mural circle; when mounted with a telescope
         on an axis and in Y's, in the plane of the meridian, a
         meridian circle or transit circle; when involving
         the principle of reflection, like the sextant, a
         reflecting circle; and when that of repeating an
         angle several times continuously along the graduated
         limb, a repeating circle.
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   4. A round body; a sphere; an orb.
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            It is he that sitteth upon the circle of the earth.
                                                  --Is. xi. 22.
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   5. Compass; circuit; inclosure.
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            In the circle of this forest.         --Shak.
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   6. A company assembled, or conceived to assemble, about a
      central point of interest, or bound by a common tie; a
      class or division of society; a coterie; a set.
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            As his name gradually became known, the circle of
            his acquaintance widened.             --Macaulay.
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   7. A circular group of persons; a ring.
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   8. A series ending where it begins, and repeating itself.
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            Thus in a circle runs the peasant's pain. --Dryden.
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   9. (Logic) A form of argument in which two or more unproved
      statements are used to prove each other; inconclusive
      reasoning.
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            That heavy bodies descend by gravity; and, again,
            that gravity is a quality whereby a heavy body
            descends, is an impertinent circle and teaches
            nothing.                              --Glanvill.
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   10. Indirect form of words; circumlocution. [R.]
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             Has he given the lie,
             In circle, or oblique, or semicircle. --J.
                                                  Fletcher.
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   11. A territorial division or district.
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   Note:

   The Circles of the Holy Roman Empire, ten in number, were
      those principalities or provinces which had seats in the
      German Diet.
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   Azimuth circle. See under Azimuth.

   Circle of altitude (Astron.), a circle parallel to the
      horizon, having its pole in the zenith; an almucantar.

   Circle of curvature. See Osculating circle of a curve
      (Below).

   Circle of declination. See under Declination.

   Circle of latitude.
       (a) (Astron.) A great circle perpendicular to the plane
           of the ecliptic, passing through its poles.
       (b) (Spherical Projection) A small circle of the sphere
           whose plane is perpendicular to the axis.

   Circles of longitude, lesser circles parallel to the
      ecliptic, diminishing as they recede from it.

   Circle of perpetual apparition, at any given place, the
      boundary of that space around the elevated pole, within
      which the stars never set. Its distance from the pole is
      equal to the latitude of the place.

   Circle of perpetual occultation, at any given place, the
      boundary of the space around the depressed pole, within
      which the stars never rise.

   Circle of the sphere, a circle upon the surface of the
      sphere, called a great circle when its plane passes
      through the center of the sphere; in all other cases, a
      small circle.

   Diurnal circle. See under Diurnal.

   Dress circle, a gallery in a theater, generally the one
      containing the prominent and more expensive seats.

   Druidical circles (Eng. Antiq.), a popular name for certain
      ancient inclosures formed by rude stones circularly
      arranged, as at Stonehenge, near Salisbury.

   Family circle, a gallery in a theater, usually one
      containing inexpensive seats.

   Horary circles (Dialing), the lines on dials which show the
      hours.

   Osculating circle of a curve (Geom.), the circle which
      touches the curve at some point in the curve, and close to
      the point more nearly coincides with the curve than any
      other circle. This circle is used as a measure of the
      curvature of the curve at the point, and hence is called
      circle of curvature.

   Pitch circle. See under Pitch.

   Vertical circle, an azimuth circle.

   Voltaic circuit or Voltaic circle. See under Circuit.


   To square the circle. See under Square.

   Syn: Ring; circlet; compass; circuit; inclosure.
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WordNet (r) 3.0 (2006):

circle of curvature
    n 1: the circle that touches a curve (on the concave side) and
         whose radius is the radius of curvature [syn: circle of
         curvature, osculating circle]