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length

1. Prosody Phonetics the metrical quantity or temporal duration of a vowel or syllable
2. the distance from one end of a rectangular swimming bath to the other
3. Prosody the quality of a vowel, whether stressed or unstressed, that distinguishes it from another vowel of similar articulatory characteristics. Thus in English beat is of greater length than in English bit
4. Cricket the distance from the batsman at which the ball pitches
5. Bridge a holding of four or more cards in a suit
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

Length

A one-dimensional extension in space. Length is one of the three fundamental physical quantities, the others being mass and time. It can be measured by comparison with an arbitrary standard; the specific one in most common usage is the international meter. In 1983, at the meeting of the Conférence Général des Poids et Mésures, the meter was redefined in terms of time and the speed of light: “The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.” This definition defines the speed of light to be exactly 299 792 458 m/s, and defines the meter in terms of the most accurately known quantity, the second. See Light, Mass, Time

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Length

 

a numerical characteristic of the extent of curves. The concept of length is defined differently for different cases. (1) The length of a line segment is the distance between its end points, measured by some segment taken as a unit of length. (2) The length of a polygonal line is the sum of the lengths of its components. (3) The length of a simple arc is the limit of the lengths of polygonal lines inscribed in the arc, when the number of components increases indefinitely and the maximum length of the components tends to zero. (4) The length of a continuous curve consisting of a finite number of simple arcs is equal to the sum of the lengths of these arcs. For example, the circumference of a circle can be obtained as the limit of the perimeters of inscribed regular polygons when the number of their sides is doubled indefinitely; it is equal to 2πR where R is the radius of the circle. Any continuous curve has finite or infinite length. If its length is finite, then the curve is said to be rectifiable. The graph (see Figure 1) of the function

for 0 <x ≤ 1 and f(x) = 0 when x = 0 is an example of a nonrectifiable curve; here the lengths of the inscribed polygonal lines increase beyond all bound as the length of the components tend to zero. If the equation of a plane curve has the form y =f(x) (a ^ x ^ b)m rectangular coordinates and the function f(x) has a continuous derivative f’(x), then the length of the curve is given by the integral

The length of a curve given in parametric form and the length of a space curve can be expressed in a similar manner.

Figure 1

To calculate the length of a curve the mathematicians of antiquity essentially used lengths of polygonal lines and passage to the limit. For them, however, such passage to the limit was only a method for calculating the length of a curve and not for defining the concept of the length of a curve, since they apparently perceived the latter as one of the elementary mathematical concepts. The necessity of defining the length of a curve became clear only in the first half of the 19th century. A full elucidation of the problem was achieved by C. Jordan. In differential geometry the length of a curve is also defined on a surface or in an arbitrary Riemannian space.

REFERENCES

Lebesgue, H. Ob izmerenii velichin, 2nd ed. Moscow, 1960. (Translated from French.)
Fikhtengol’ts, G. M. Kurs differentsial’nogo i integral’nogo ischisleniya, 7th ed. vol. 2. Moscow, 1969.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

length

[leŋkth]
(mechanics)
Extension in space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Note, FA, filtered air; PCL, pacing cycle length; S1, normal pacing stimuli; S2, premature stimulus; SHS, secondhand smoke.
An increase in incline affected all of the cycle characteristics monitored, with reductions in cycle velocity, cycle length and pole swing time (both absolute and relative to cycle time) and enhancement of poling time and external power output.
We set the error tolerance to [10.sup.-6] and vary the cycle length, letting m[member of]{25,50,100,150}.
When cycle length is small, all the incoming frames can be transmitted with waiting less after they arrive in the network as shown in Fig.
In this work, one of the most important objectives is to find the relationship between the uranium enrichment and the cladding thickness without reduction in cycle length. It is thus not necessary to analyze the reactivity of combinations with Afccore far away from zero.
At the optimal solutions, (1) R is higher for lost sales (as expected, because in our example, backlog cost and lost sales cost are the same, so it is only natural that the cycle service level would be set higher (less PS) to try to prevent shortages for lost sales), (2) Q is higher for backlog because it must satisfy demands during stockout, (3) higher R leads to higher EO and PO for lost sales, whereas higher Q leads to higher holding cost for backlog, and (4) although backlog has a higher total cost, it also has a longer cycle length, which leads to a lower average total cost per period.
When cycle length T is large, the discretization of model constraints may introduce huge errors.
It exhibited as a focal AT with a short cycle length (70% TCL) when completed the three-dimensional electroanatomic map in LA.
And the team observed gradual changes in brain wave patterns, such as increasing sleep cycle length over the course of a night, which would be unexpected if the lizards were constantly waking up.
The work of one iteration is naively the cycle length, but can be reduced to O(log n) with a fast data structure, yielding O(m log [n.sup.2] log log n) total work.
Frank Guinta (R-N.H.) and Ruben Hinojosa (D-Texas) called upon the agency to extend the exam cycle length for well-capitalized credit unions and provide a timeline for its efforts.
The cycle length of 2000 ms was used in this study since it was closer to normal human beat rhythm than the length of 4000 ms used in the experiments from Guo et al.