length

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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 It might be outdated or ideologically biased.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 classic literature ?
Agitation of spirit kept me awake for many long hours; but at length I again slumbered.
I now lay upon my back, and at full length, on a species of low framework of wood.
Wearied at length with observing its dull movement, I turned my eyes upon the other objects in the cell.
At length the King, recovering from his astonishment at recognising the brother who had been lost some years before, exclaimed, 'Yes, you are indeed my brother, and now that I have found you, take the throne to which I have no longer a right.' So saying, he respectfully kissed the Prince's hand.
I mean that when you see a Woman, you ought -- besides inferring her breadth -- to see her length, and to SEE what we call her HEIGHT; although that last Dimension is infinitesimal in your country.
When we in Flatland see a Line, we see length and BRIGHTNESS.
At length, one of the men, more exhausted than the rest, threw himself upon the grass, and declared he could go no further.
Disease crept over both mind and body, he was tortured by pain, and when at length the pain left him he sank into torpor.
I succeeded so well in this endeavor that, in a few days, the creature bestowed upon me various tokens of his favor, and in the end even went to the trouble of teaching me the rudiments of what it was vain enough to denominate its language; so that, at length, I was enabled to converse with it readily, and came to make it comprehend the ardent desire I had of seeing the world.
"'The beast,' continued Sinbad to the caliph, 'swam, as I have related, up hill and down hill until, at length, we arrived at an island, many hundreds of miles in circumference, but which, nevertheless, had been built in the middle of the sea by a colony of little things like caterpillars'"
I took a step, and lo, away it scud with an elastic spring over the snow-crust, straightening its body and its limbs into graceful length, and soon put the forest between me and itself -- the wild free venison, asserting its vigor and the dignity of Nature.
On the following day the search was resumed, and the poor fellow was at length discovered lying beneath a group of rocks, his legs swollen, his feet torn and bloody from walking through bushes and briars, and himself half- dead with cold, hunger, and fatigue.