# length

(redirected from lengthy)
Also found in: Dictionary, Thesaurus, Medical, Legal.
Related to lengthy: lengthily

## 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

## 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

## 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.

## length

[leŋkth]
(mechanics)
Extension in space.
References in periodicals archive ?
Obviously a lengthy custodial sentence will follow.
Commissioner told that development schemes for Rahim Yar Khan district include restoration of 20 kilometers lengthy road from Khanpur to Bagh-o-Bahar with a cost of Rs 259.
An investigation by DOT s Aviation Enforcement Office found that on January 2 into January 3, 2014, 16 Southwest flights experienced lengthy tarmac delays at Midway in excess of three hours.
Speaker Ishwar Das Rohani said the department officials should have consulted him before sending such a lengthy reply.
The four-year-old faces six rivals, one of which, the Jonathan Jay-trained Carlton Scroop, is also returning after a lengthy break of 275 days.
However, following the lengthy negotiations to reach this point it is also possible the final agreement may not come until later in the month.
This is not normally as lengthy or complicated a process as you fear.
The 20-year-old feared an operation and lengthy lay-off after suffering tendinitis in his right knee.
And football players at XYZ were able to handle the increased demands of playing lengthy seasons, even when those lengthy seasons conflicted with the final exam schedule, with no detriment in their grades.
After a lengthy federal investigation, the perpetrators were apprehended and tried for their crimes, giving occasion for journalist Matt Rasmussen to investigate the motivations of the ELF terrorists.
GOP lawmakers, for the most part, said they believe the media has hyped the role of religion in modern politics and said they see little noteworthy about lengthy House floor discussions about God.
I wonder why such lengthy deliberation was necessary.

Site: Follow: Share:
Open / Close