length of a curve

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length of a curve

[′leŋkth əv ə ′kərv]
(mathematics)
A curve represented by x = x (t), y = y (t) for t1tt2, with x (t1) = x1, x (t2) = x2, y (t1) = y1, y (t2) = y2, has length from (x1, y1) to (x2, y2) given by the integral from t1 to t2 of the function √((dx / dt)2+ (dy / dt)2).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The mapping [alpha], [alpha](x,y) = (c(x),y), is an isometric immersion of [R.sup.2] into [R.sup.4], where c(x) is a curve in [R.sup.3] [congruent to] [R.sup.3] x{0}, x being the arc length parameter.
Furthermore, Chapman (2017) refers to two measurements: tooth row arc length and inner alveolar arc length.
Violet blocks from the group of elements of the perturbation setting simulate the deterministic and random perturbations along the arc length which arise during the arc furnace operation at arc gaps at different technological stages of melting.
For instance, users have more options in dimensions and annotation types, such as Chamfer, Arc Length, Hole, Center Line, and Linear Radius.
It can be concluded that with the accumulation of the observation arc length, the accuracy of the orbit prediction of these three strategies is on the same level.
Observation conditions such as frequency of track and arc length can affect the orbit estimation accuracy.
[theta]([c.sub.1], [c.sub.2]) is used to express the spherical distance between [c.sub.1] and [c.sub.2], that is, the arc length connecting [phi]([c.sub.1]) and [phi]([c.sub.2]) on the Riemann ball; then
Alfonso, "Long-term follow-up of intrastromal corneal ring segments (210-degree arc length) in central keratoconus with high corneal asphericity," Cornea, vol.
In this paper, we use arc length parametrization to be the parametrization for the task and four-bar coupler curve.
In general, the arc voltage in direct current nontransferred plasma torch is approximately linearly dependent on the arc length which is determined by the balance between electromagnetic force and flow drag force [26].
Call that the inside arc length. Now, add the thickness of the part to that inside radius and calculate the arc length again to find the outside arc length.