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Topic: Radius of curvature

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	Curvature - Wikipedia, the free encyclopedia
		There is a key distinction between extrinsic curvature which is defined for objects embedded in another space (usually a Euclidean space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature which is defined at each point in a differential manifold.
		For a plane curve C, the curvature at a given point P has a magnitude equal to the reciprocal of the radius of an osculating circle (a circle that "kisses" or closely touches the curve at the given point), and is a vector pointing in the direction of that circle's center.
		Unlike Gauss curvature, the mean curvature depends on the embedding, for instance, a cylinder and a plane are locally isometric but the mean curvature of a plane is zero while that of a cylinder is nonzero.
	en.wikipedia.org /wiki/Curvature (1206 words)

	Radius - Wikipedia, the free encyclopedia
		In classical geometry, a radius of a circle or sphere is any line segment from its center to its boundary.
		More generally—in geometry, engineering, graph theory, and many other contexts—the radius of something (e.g., a cylinder, a polygon, a graph, or a mechanical part) is the distance from its center or axis of symmetry to its outermost points.
		The relationship between the radius and the circumference of a circle is
	en.wikipedia.org /wiki/Radius (159 words)

	Earth radius - Facts, Information, and Encyclopedia Reference article
		The radius of Earth (or any planet) is the distance from its centre to a point on its surface at mean sea level.
		The Earth's equatorial radius, or semi-major axis, is the distance from its centre to the equator and equals 6,378.135 km (≈3,963.189 mi; ≈3,443.917 nm).
		It is this radius that would be used to approximate the ellipsoid's average great ellipse (i.e., this is the equivalent spherical "great-circle" radius of the ellipsoid). For Earth, $Q_r$ equals 6,372.795477598 km (≈3,959.871 mi; ≈3,441.034 nm).
	www.startsurfing.com /encyclopedia/e/a/r/Earth_radius.html (366 words)

	Radius of Curvature (Site not responding. Last check: 2007-11-01)
		The radius of curvature is the reciprocal of curvature, as defined in the previous section.
		The radius of the osculating circle is the radius of curvature.
		The curvature is the norm of the accelleration, which is 1/r.
	www.mathreference.com /ca-path,radius.html (408 words)

	Curveball Trajectory (Site not responding. Last check: 2007-11-01)
		The details of how the force is generated are fairly complex, but the magnitude of the force F depends on the radius of the ball b, the spin of the ball G, the velocity V of the pitch, and the density r of the air.
		The radius of curvature R of the flight path depends on the velocity V of the pitch and the acceleration a produced by the side force.
		At higher altitudes, the density r is lower producing a larger radius of curvature and a straighter path.
	www.grc.nasa.gov /WWW/K-12/airplane/btraj.html (624 words)

	Radii on the Ellipsoid
		For converting degrees of latitude to linear units of Y, the radius used is known as the meridional radius of curvature.
		Conceptually, it is the simpler of the two radii involved, and it is, essentially, the radius of curvature, at a specific latitude, of the ellipse used to generate the ellipsoid.
		The second radius, the one which will convert a small change in longitude to an equivalent change in X is known as the transverse radius of curvature of an ellipsoid.
	www.mentorsoftwareinc.com /CC/gistips/TIPS0899.HTM (1971 words)

	The History of Curvature (Site not responding. Last check: 2007-11-01)
		Huygens "attempt[ed]" to define the radius of curvature of the involute as the distance between the points of contact between the involute with the string and evolute with the string (Coolidge 377).
		He stated that the degree of curvature is equivalent to the second fluxion of the curve, and this is a measure of "deflection from [the] tangent" (Simpson 53).
		Leonhard Euler is the mathematician responsible for the important theorem that the magnitude of curvature equals the magnitude of the second derivative of a parameterization at a point (McCleary 67).
	www.brown.edu /Students/OHJC/hm4/k.htm (3531 words)

	Circle and Radius of Curvature
		The standard derivation of the formula for radius curvature involves the rate of change of the unit tangent vector.
		The radius of curvature and formulas for the location of its center are simultaneously derived.
		The ordinate of the circle of curvature is
	math.fullerton.edu /mathews/n2003/CurvatureMod.html (766 words)

	Oscar Gonzalez: Global curvature ... (Site not responding. Last check: 2007-11-01)
		During a lunch-time discussion on the ideal shapes of knots and such, the concept of the "global curvature function" of a space curve was born.
		Moreover, global curvature is connected to the writhing number of a space curve and has applications in the study of self-contact and packing problems for rods.
		Moreover, global radius of curvature is connected to the writhing number of a space curve and has applications in the study of self-contact problems for rods.
	www.ma.utexas.edu /~og/curvature.html (1621 words)

	Project Links \| Curvature Module (Site not responding. Last check: 2007-11-01)
		Since the curvature of a circle of radius R is the constant value 1/R, it is natural to use circles to help define curvature.
		Dangerous Bend: The curvature is the reciprocal of the radius of curvature, so the radius of curvature is a local maximum when the curvature is a local minimum, and vice versa.
		At vertices the curve is either locally inside the osculating circle (at local maximums of curvature) or locally outside the osculating circle(at local minimums of curvature).
	www.ibiblio.org /links/devmodules/curvature/html/osculating_concept.html (358 words)

	POLITICALLY CORRECT RADIUS OF CURVATURE (Site not responding. Last check: 2007-11-01)
		A center of curvature that is to the left of the surface gives a negative radius, and the surface is concave.
		In the second lens above, the radius of the third surface is negative, and the radius of the fourth surface is positive; the end result is that both surfaces have a negative sign when the formula is computed, and the result is negative the sum of the surface powers.
		In the third lens the radius of the fifth surface is positive as is the sixth surface; when the back surface power is subtracted from the front surface power the result is what we get the 'Opticians' way.
	www.nfos.org /degree/opt11/module_06c1.html (318 words)

	Curvature classes
		The measure for the radius of curvature implied by a pair of tangents given by [
		This tedious process adds to the complexity of computing the curvature class partitioning function, but since this computation is performed offline, it does not add much to the overall complexity of the trace inference algorithm.
		The curvature classes were determined by the following set of radius limits: 4, 6, 12.
	www.cim.mcgill.ca /~cathy/a1report766/node5.html (282 words)

	The Curvature of the Universe Background (Site not responding. Last check: 2007-11-01)
		The Earth's radius is a length that best describes the rate of curvature of the surface of the Earth.
		The radius is the important factor in the circumference, surface area and volume of the Earth.
		It is important to understand the role of the radius in an easily understandable situation since this concept will reappear when we study the curvature of the universe.
	www.astro.princeton.edu /~clark/CurveUBkgd.html (2215 words)

	Tangent vector and Curvature (Site not responding. Last check: 2007-11-01)
		Curvature is normally represented by the Greek Symbol Kappa, but I'll use a capital K here.
		Similarly, the radius of curvature is represented by a Greek rho, I'll use a lowercase r.
		The concept of curvature comes from fitting a circle tangent to the curve in at the point of question.
	omega.albany.edu:8008 /calc3/curves1-dir/lecture.html (285 words)

	Zygo Corporation - Radius of Curvature Options - gpi accessory mounts option
		The Digital Radius Scale consists of a magnetic scale for position feedback, mounted on a 1-meter guide bar that is fixed to the granite or optical table.
		The distance the mount moves from cat's eye position to confocal position is the radius of curvature of the part under test.
		The distance the mount moves from catseye position to confocal position is the radius of curvature of the part under test.
	www.zygo.com /?/products/gpi_acc/rad_crv/rad_crv.htm (521 words)

	CURVATURE OF STEMS
		The radius of this circle is the radius of curvature.
		The radius of curvature, R, and curvature, k, are related to one another.
		Therefore curvature, k, is the reciprocal of the radius of curvature, R. Interpretation: Scientists can take time-lapse photographs of plant stems or roots in order to quantify curvature over time, and under different treatments.
	www.tiem.utk.edu /~gross/bioed/webmodules/stemcurvature.html (766 words)

	Circle of Curvature and Radius of Curvature (Site not responding. Last check: 2007-11-01)
		Circle of curvature is a circle that "fit" the curve at a point.
		If the curve is turning sharply, the radius of curvature is small and if the curve is turning slowly, the radius of curvature is large.
		Applet 1 shows change of the radius of curvature on y=cos x.
	www.ies.co.jp /math/java/calc/curve/curve.html (67 words)

	Sphericity and radius of curvature measurements
		Firstly, the radius of curvature of the convex surface under test must be less than the back focal length of the transmission sphere; and secondly, the radius of curvature of the surface under test divided by the clear aperture, i.e., the R/number, should be approximately equal to the f/number of the transmission sphere.
		The center of curvature of the test surface is interferometrically made to coincide with the focus of the spherical wave emanating from the transmission sphere.
		For cases where extreme accuracy is required (1 micron or 0.001%) an Interferometric Radius Slide is available that inputs distance measurements directly to the interferometer’s processor and is corrected for focus errors.
	www.phase-shift.com /products/interferometer-sphericity.shtml (934 words)

	Re: What governs the radius of curvature of a liquid meniscus?
		The factors governing the radii of curvature are the surface tension, rho, the gravitational constant, g, the densities of the two liquids, and the geometry of the surfaces that constrain the film.
		where r1 would be the radius of the rod and r2 would be the radius of curvature of the "meniscal" surface along a radius from the rod's axis.
		The pressure (exterted by the force either upward or downward between the rod and the contact ring) would equal the downward force, rhogy, where y is the height above the main surface at a point on the meniscus.
	www.madsci.org /posts/archives/mar97/853785360.Ph.r.html (297 words)

	helix and radius of curvature
		If it's circling around the z axis, the radius of it's projection onto the xy axis is a circle of radius r.
		You know the radius projected onto the x-y plane, and also that d is proportional to the period.
		I guess what I really want to know is what is the radius R of the circle that is made from the length of a string that is wound around a cyninder with radius r as it spans a distance d (along the longitudinal axis of the cylinder) to make one cycle around the cylinder.
	www.physicsforums.com /showthread.php?t=94758 (707 words)

	The Curvature of Stellar Orbits
		For nearby stars this difference will always be negligible and thus the curvature of their orbits is of no consequence to GAIA.
		Another way to look at this problem, without resorting to the approximation of constant acceleration in time, is to realize that the relevant parameter is the curvature of the relative orbit of the star and the Sun.
		is the radius of curvature of the relative orbit.
	www.rssd.esa.int /SA-general/Projects/GAIA_files/LATEX2HTML/node149.html (263 words)

	- Degrees curvature versus radius in feet
		I have an old New York Central specification sheet for the ALCO RS-3 that lists the sharpest curve that the engine could operate on was 21 degrees.
		One of my "treasures" is a Fairbanks-Morse brochure entitled, "The Lackawanna Story." Brochure was a sales piece for the F-M Train Master, which was not a small locomotive (around 67 feet over couplers) for the time.
		With HO-scale, 212' radius is about 29 inches.
	www.trainnet.org /dcforum/DCForumID28/37.html (223 words)

	Curvature drifts
		Curvature of magnetic field lines can also cause plasma particles to drift.
		As the particle moves along a curved magnetic field line it experiences a centrifugal force due to the field curvature, and therefore drifts perpendicular to both the centrifugal force and
		This final form relates the radius of curvature to the magnetic field using Ampere's Law (assuming no plasma currents).
	www.physics.usyd.edu.au /~cairns/teaching/lecture2/node8.html (140 words)

	base curve - Contact lense information for those who choose not to wear glasses.
		Typical values are from 7.Base curve@Everything2.com In the fast paced and thrilling world of optics, the base curve is one of the The base curve is the curvature, in diopters, of the front of the lens.
		RELATED ENTRIES Base curve@Everything2.com In the fast paced and thrilling world of optics, the base curve is one of the The base curve is the curvature, in diopters, of the front of the lens.
		The base curve is the radius of the sphere that the back of the contact lens describes.
	www.ispacs2005.com /base_curve.html (472 words)

	Curvature, Center Of Curvature (Site not responding. Last check: 2007-11-01)
		Following figure shows two circles of curvature at x=-3 and x=2.5 on the graph of function y=cos(x).
		The curvature and the center of curvature can also be calculated.
		Curvature circle: Position: x=-3, y=-.9899925 Curvature:.9611386 The radius of curvature circle: 1.040433 Center of curvature circle: x=-3.145385, y=4.023233E-02 Position: x=2.5, y=-.8011436 Curvature:.5061505 The radius of curvature circle: 1.975697 Center of curvature circle: x=3.514582, y=.8941441
	www.graphnow.com /details/curvature.html (114 words)

	Detectability of Extraterrestrial Technological Activities by Guillermo A. Lemarchand
		The trajectories it follows depend on the local curvature of the Universe, and thus on the local distribution of matter (gravitational lenses), extinction affecting different wavelengths unequally, neutral hydrogen absorbing all radiation below the Lyman limit (912 Angstrom), and absorption and scattering by interstellar dust, which is more severe at short wavelengths.
		The volume of such a sphere would be 4 pi r(squared) S, where r is the radius of the sphere (1 A.U.) and S the thickness.
		The Dyson Sphere has a radius of 1.5x10 to the 8 power kilometers and is 3 meters thick.
	www.coseti.org /lemarch1.htm (8947 words)

	Road Curvature Prediction (Site not responding. Last check: 2007-11-01)
		Currently, road curvature is determined by kinematic means alone using yaw rate sensing, steering wheel angle and differential wheel speeds.
		Using vehicle kinematics alone to determine impending road curvature is fine for road sections of constant radius (click on thumbnail to see larger image):
		If a database of impending road position could be stored within the ACC vehicle and the current position and bearing could be determined in real-time, then it may be possible to predict curvature for any road layout/curvature see RCP Operation.
	users.powernet.co.uk /brig/index.htm (133 words)

	Zygo Corporation - Radius of Curvature Measurement - About Resolution & Accuracy
		Radius of Curvature Measurement - About Resolution and Accuracy
		Accuracy depends upon many factors, such as: the straightness of the guide bar, the flatness of the table or granite, the installation and alignment of the scale to the interferometer, and environmental conditions.
		Typically, the smaller the radius of the part, the greater the accuracy of the measurement.
	www.zygo.com /products/gpi_acc/rad_crv/res_acc.htm (107 words)

	Origin Technologies LaserGauge Radius Application
		Radius of curvature - the radius of a curved feature captured on the surface profile can be measured by selecting two points on the curve.
		Factory - quality measurements of parts machined to specification.
		For on-line applications, the Series 3000 and RS400 would be used.
	www.origintech.com /Radius.html (80 words)

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