Aliquot

Aliquot

In mathematics, an aliquot part (or simply aliquot) of an integer is any of its integer proper divisors. For instance, 2 is an aliquot of 12. The sum of all the aliquots of an integer "n" is the value s("n") = σ("n") - "n" , where σ("n") is the sum of divisors function.

In chemistry, an aliquot is usually a portion of a total amount of a solution.

The word comes from the Latin "aliquoties", "several times".

In pharmaceutics, aliquot refers to a method of measuring ingredients below the sensitivity of a scale. For example, if a scale is inaccurate for samples under 120 mg, but the prescription calls for only 40 mg of drug, an aliquot must be done. This involves adding active ingredient and a proportional amount of diluent to make a "stock" supply. In this case, 120 mg active drug must be weighed and mixed with diluent. Once this stock supply is made, at least 120 mg of this mixture will be taken out and used (as long as this portion contains exactly 40 mg of active drug).

Music

In the construction of string instruments often aliquot parts of the scale length are being used to enhance the timbre of musical instruments. In pianos the aliquot stringing system is sometimes used. Non-Western traditional instruments with sympathetic strings make also use of timbre enhancing based on aliqout stringing and string resonance. The aliquot position (1/7th of the scale length) of the bridge on a violin is also important for the sound of the instrument.

Land Surveying

An aliquot part, in the U.S. Public Land Survey System, is the standard subdivision of area of a section, (a.k.a. a half section, quarter section, or quarter-quarter section). One section of land is a square mile, containing 640 acres (but actual lines as run in the field can produce varying area totals).

Egyptian fraction arithmetic

The aliquot parts of the denominator of the first partition of 2/p conversions to Egyptian fractions was used 25 times in the 1650 BCE RMP 2/n table. The method was in use as late as the Liber Abaci, a text written by Fibonacci in 1202 AD. F. Hultsch first noticed the aliquot part use in 1895. E.M. Bruins confirmed its use in 1945. Today, the use of aliquot parts in Egyptian fraction arithmetic is know as the Hultsch-Bruins method.

Aliquant

By contrast, an aliquant part (or simply aliquant) of a positive integer "n" is an integer that is not an exact divisor of "n". Thus the aliquants of an integer "n" are the positive integers "m" less than "n" such that gcd("m","n") < "m". For example, the aliquants of 16 are 3, 5, 6, 7, 9, 10, 11, 12, 13, 14 and 15.

All integers that are less than "n" but greater than half of "n" are aliquants of "n". Every positive integer less than "n" is either an aliquant or an aliquot of "n", so the number of aliquants of "n" and the number of aliquots of "n" sum to "n" - 1.

ee also

* aliquot sequence
* aliquot sum
* amicable number

External links

* [http://www.cut-the-knot.org/Curriculum/Arithmetic/Aliquot.shtml Aliquot Game] at cut-the-knot


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Aliquot — Al i*quot, a. [L. aliquot some, several; alius other + quot how many: cf. F. aliquote.] (Math.) An aliquot part of a number or quantity is one which will divide it without a remainder; thus, 5 is an aliquot part of 15. Opposed to {aliquant}.… …   The Collaborative International Dictionary of English

  • aliquot — al·i·quot / a lə ˌkwät, kwət/ adj [Medieval Latin aliquotus contained an exact number of times in something else, from Latin aliquot some, several]: of, relating to, or being a fraction or percentage of a whole may deduct an aliquot part of the… …   Law dictionary

  • aliquot — [al′i kwət, al′ikwät΄] adj. [Fr aliquote, prob. via ML aliquota (fem.) < L aliquot, some, several < alius, other + quot, how many] 1. designating or of a portion, part, or sample of a chemical, medicine, etc. 2. Math. designating a part of… …   English World dictionary

  • aliquot — <zu lat. aliquot »einige«>: 1. ohne Rest teilend (der aliquote Teil einer Zahl ist jeder ihrer Teiler, z. B. 2 zur Zahl 6; Math.); Ggs. ↑aliquant. 2. die Aliquottöne betreffend (Mus.) …   Das große Fremdwörterbuch

  • aliquot — ► NOUN 1) a portion of a larger whole, especially a sample taken for chemical analysis or other treatment. 2) (also aliquot part or portion) Mathematics a quantity which can be divided into another a whole number of times. ► VERB ▪ divide into… …   English terms dictionary

  • aliquot — aliquot. См. аликвота. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь.

  • aliquot: — aliquot: [al ee kwoh] adj.    a definite fractional share, usually applied when dividing and distributing a dead person s estate or trust assets.    See also: share Law dictionary. EdwART. 2013 …   Law dictionary

  • aliquot — adjective Etymology: Medieval Latin aliquotus, from Latin aliquot some, several, from alius other + quot how many more at else, quote Date: 1570 1. contained an exact number of times in something else used of a divisor or part < 5 is an aliquot… …   New Collegiate Dictionary

  • aliquot — In chemistry and immunology, pertaining to a portion of the whole; loosely, any one of two or more samples of something, of the same volume or weight. [L. a few, several] * * * al·i·quot al ə .kwät adj being an equal fractional part (as of a… …   Medical dictionary

  • Aliquot — Die Aliquoten (v. lat. aliquot „einige, ein paar“) sind bei Musikinstrumenten die Hilfssaiten und stimmen: Aliquotsaiten sind bei einem Saiteninstrument, wie etwa dem Baryton, zusätzliche Begleitsaiten, die meist unterhalb der eigentlichen… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”