* Radius of curvature ( disambiguation ), various meanings

* Radius of curvature

* Radius of curvature ( applications )

Radius of curvature ( r )

* Focal Plane Radius of curvature 966. 3mm

* Radius of curvature

* Radius of curvature ( optics )

* Radius of curvature ( applications )

* Radius affects the size of the edges to be enhanced or how wide the edge rims become, so a smaller radius enhances smaller-scale detail.

Radius is a straight line or distance from the center to the edge of a curve.

The curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points.

For example, an ant living on a sphere could measure the sum of the interior angles of a triangle and determine that it was greater than 180 degrees, implying that the space it inhabited had positive curvature.

Various generalizations capture in an abstract form this idea of curvature as a measure of holonomy ; see curvature form.

These generalizations of curvature underlie, for instance, the notion that curvature can be a property of a measure ; see curvature of a measure.

* Curvature of a measure for a notion of curvature in measure theory

Thinking of curvature as a measure, rather than as a function, Descartes ' theorem is Gauss – Bonnet where the curvature is a discrete measure, and Gauss – Bonnet for measures generalizes both Gauss – Bonnet for smooth manifolds and Descartes ' theorem.

If a curved surface is developed upon any other surface whatever, the measure of curvature in each point remains unchanged.

It is an intrinsic measure of curvature, i. e., its value depends only on how distances are measured on the surface, not on the way it is isometrically embedded in space.

* Sheer ( ship ), a measure of longitudinal deck curvature in naval architecture

The infinitesimal change of the vector is a measure of the curvature.

The spaceflight phase lasted until 2005 ; its aim was to measure spacetime curvature near Earth, and thereby the stress – energy tensor ( which is related to the distribution and the motion of matter in space ) in and near Earth.

Sensors measure the force and moment generated, and a correction is made to account for the curvature of the track.

A keratometer may be used to measure the curvature of the steepest and flattest meridians in the cornea's front surface.

In mathematics, the mean curvature of a surface is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space.

That is, curvature does not depend on how the surface might be embedded in 3-dimensional space or 2-dimensional space.

In higher dimensions, the Riemann curvature tensor is an important pointwise invariant associated to a Riemannian manifold that measures how close it is to being flat.

Two interesting experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket.

Geometrically, the curvature measures how fast the unit tangent vector to the curve rotates.

This generalization of curvature depends on how nearby test particles diverge or converge when they are allowed to move freely in the space ; see Jacobi field.

So for instance if you have a sphere with a " dent ", then its total curvature is 4π ( the Euler characteristic of a sphere being 2 ), no matter how big or deep the dent.

That is, curvature does not depend on how the surface might be embedded in 3-dimensional space.

Snell calculated how the planar formulae could be corrected to allow for the curvature of the earth.

Apollonius's genius reaches its highest heights in Book v. Here he treats of normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ); discusses how many normals can be drawn from particular points ; finds their feet by construction ; and gives propositions that both determine the center of curvature at any point and lead at once to the Cartesian equation of the evolute of any conic.

Toponogov's theorem affords a characterization of sectional curvature in terms of how " fat " geodesic triangles appear when compared to their Euclidean counterparts.

Quenching puts an enormous amount of stress on the metal and if cooled unevenly, it can warp the metal, which is how some swords acquire their curvature ; this is called differential hardening.

The EFE can then be interpreted as a set of equations dictating how matter / energy determines the curvature of spacetime.

The Frenet-Serret formulas show that there is a pair of functions defined on the curve, the torsion and curvature, which are obtained by differentiating the frame, and which describe completely how the frame evolves in time along the curve.

In Riemannian geometry, the geodesic curvature of a curve lying on a submanifold of the ambient space measures how far the curve is from being a geodesic.

* On the contrary the normal curvature depends strongly on how the submanifold lies in the ambient space, but marginally on the curve: only depends on the point on the submanifold and the direction, but not on.

While it is possible to obtain a detailed numerical model of electrowetting by considering the precise shape of the electrical fringing field and how it affects the local droplet curvature, such solutions are mathematically and computationally complex.

Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes.

Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i. e. how the duration of a bond changes as the interest rate changes.

Einstein's theory, depending on how much of the curvature one wants to reexpress

The second equation describes how the stress-energy tensor and scalar field together affect spacetime curvature.

The platform gap is mainly caused by the curvature of the station and how the train enters the station area.