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Radius of curvature

Radius Ra"di*us, n.; pl. L. Radii; E. Radiuses. [L., a staff, rod, spoke of a wheel, radius, ray. See Ray a divergent line.] 1. (Geom.) A right line drawn or extending from the center of a circle to the periphery; the semidiameter of a circle or sphere. 2. (Anat.) The preaxial bone of the forearm, or brachium, corresponding to the tibia of the hind limb. See Illust. of Artiodactyla. Note: The radius is on the same side of the limb as the thumb, or pollex, and in man it so articulated that its lower end is capable of partial rotation about the ulna. 3. (Bot.) A ray, or outer floret, of the capitulum of such plants as the sunflower and the daisy. See Ray, 2. 4. pl. (Zo["o]l.) (a) The barbs of a perfect feather. (b) Radiating organs, or color-markings, of the radiates. 5. The movable limb of a sextant or other angular instrument. --Knight. Radius bar (Math.), a bar pivoted at one end, about which it swings, and having its other end attached to a piece which it causes to move in a circular arc. Radius of curvature. See under Curvature.

Radius Ra"di*us, n.; pl. L. Radii; E. Radiuses. [L., a staff, rod, spoke of a wheel, radius, ray. See Ray a divergent line.] 1. (Geom.) A right line drawn or extending from the center of a circle to the periphery; the semidiameter of a circle or sphere. 2. (Anat.) The preaxial bone of the forearm, or brachium, corresponding to the tibia of the hind limb. See Illust. of Artiodactyla. Note: The radius is on the same side of the limb as the thumb, or pollex, and in man it so articulated that its lower end is capable of partial rotation about the ulna. 3. (Bot.) A ray, or outer floret, of the capitulum of such plants as the sunflower and the daisy. See Ray, 2. 4. pl. (Zo["o]l.) (a) The barbs of a perfect feather. (b) Radiating organs, or color-markings, of the radiates. 5. The movable limb of a sextant or other angular instrument. --Knight. Radius bar (Math.), a bar pivoted at one end, about which it swings, and having its other end attached to a piece which it causes to move in a circular arc. Radius of curvature. See under Curvature.

Radius of curvature

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. The elegant curvature of their fronds. --Darwin. 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. 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.

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. The elegant curvature of their fronds. --Darwin. 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. 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.

- differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best...

- Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located...

- perpendicularly (east–west). The corresponding radius of curvature depends on the location and direction of measurement from that point. A consequence is...

- that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The...

- railroads that cannot take the sharper curvature. For the handling of long freight trains, a minimum 574-foot (175.0 m) radius is preferred. The sharpest curves...

- portion of the curve is traveled. Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature...

- normal plane. Profile radius of curvature is the radius of curvature of a tooth profile, usually at the pitch point or a point of contact. It varies continuously...

- portion of it. A sphere has a single radius of curvature, which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary...

- Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point...

- Bend radius, which is measured to the inside curvature, is the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging...

- Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located...

- perpendicularly (east–west). The corresponding radius of curvature depends on the location and direction of measurement from that point. A consequence is...

- that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The...

- railroads that cannot take the sharper curvature. For the handling of long freight trains, a minimum 574-foot (175.0 m) radius is preferred. The sharpest curves...

- portion of the curve is traveled. Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature...

- normal plane. Profile radius of curvature is the radius of curvature of a tooth profile, usually at the pitch point or a point of contact. It varies continuously...

- portion of it. A sphere has a single radius of curvature, which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary...

- Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point...

- Bend radius, which is measured to the inside curvature, is the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging...

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