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]

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. [1913 Webster] The elegant curvature of their fronds. --Darwin. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster]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-.] [1913 Webster] 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. [1913 Webster] 2. The line that bounds such a figure; a circumference; a ring. [1913 Webster] 3. (Astron.) An instrument of observation, the graduated limb of which consists of an entire circle. [1913 Webster] 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. [1913 Webster] 4. A round body; a sphere; an orb. [1913 Webster] It is he that sitteth upon the circle of the earth. --Is. xi. 22. [1913 Webster] 5. Compass; circuit; inclosure. [1913 Webster] In the circle of this forest. --Shak. [1913 Webster] 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. [1913 Webster] As his name gradually became known, the circle of his acquaintance widened. --Macaulay. [1913 Webster] 7. A circular group of persons; a ring. [1913 Webster] 8. A series ending where it begins, and repeating itself. [1913 Webster] Thus in a circle runs the peasant's pain. --Dryden. [1913 Webster] 9. (Logic) A form of argument in which two or more unproved statements are used to prove each other; inconclusive reasoning. [1913 Webster] 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. [1913 Webster] 10. Indirect form of words; circumlocution. [R.] [1913 Webster] Has he given the lie, In circle, or oblique, or semicircle. --J. Fletcher. [1913 Webster] 11. A territorial division or district. [1913 Webster] Note: The Circles of the Holy Roman Empire, ten in number, were those principalities or provinces which had seats in the German Diet. [1913 Webster] 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. [1913 Webster]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]