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...

Earth's radius involve the radius of curvature. A few definitions yield values outside the range between the polar radius and equatorial radius because...

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...

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...

_{1}\kappa _{2}.} The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat...

railways 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...

length of arc or chord. Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature, but...

that the local thickness is at most equal to the local radius of curvature. The thickness of a link is defined as τ(L)=infτ(x).{\displaystyle \tau (L)=\inf...

When R = 0, the torus degenerates into a sphere with radius r. The greatest radius of curvature of the toric lens surface, R + r, corresponds to the smallest...

kinematics of curved motion it is known that an object moving at tangential speed v along a path with radius of curvature r accelerates toward the center of curvature...

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...

life. The smaller the bend radius, the greater the material flexibility (as the radius of curvature decreases, the curvature increases). The diagram to...

geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal...

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...

that plane. Bend radius Filling radius in Riemannian geometry Radius of convergence Radius of convexity Radius of curvature Radius of gyration Semidiameter...

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...

and radius of curvature ρ ( φ ) = 8 3 a sin ⁡ φ 2 . {\displaystyle \rho (\varphi )={\tfrac {8}{3}}a\sin {\tfrac {\varphi }{2}}\,.} The proofs of these...

capillary, the radius of curvature will also increase, creating a flatter interface. (Note: This is not to say that larger radii of curvature result in more...

surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinite. If d...

in Book 1 of Philosophiæ Naturalis Principia Mathematica as Proposition 30. The focal length of a parabola is half of its radius of curvature at its vertex...

the initial radius of the stream. When the wave number is such that the radius of curvature of the wave dominates that of the radius of the stream, such...

of curvature so obtained would be related to the equatorial radius and the polar radius, respectively a and b (see: Earth polar and equatorial radius...

and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and...

negative radius of curvature, so f = − R 2 , {\displaystyle f=-{R \over 2},} where R is the radius of curvature of the mirror's surface. See Radius of curvature...

the parcel position and the centre of curvature is the radius of curvature R at that position. The radius of curvature approaches an infinite length at...

the assumption that the lens is relatively thin.) The radius of curvature R {\displaystyle R} of the surface can be obtained from the optical power given...

curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve...

measurement of the radius of curvature of a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface...

at the plane z along the beam, w0 = w(0) is the waist radius, R(z) is the radius of curvature of the beam's wavefronts at z, and ψ(z) is the Gouy phase...

and radius of curvature R, separated by some distance d. For the purposes of ray tracing, this is equivalent to a series of identical thin lenses of focal...