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Difference between revisions of "Aliquot ratio"

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''aliquot fraction''
 
''aliquot fraction''
  
A fraction of the type <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011920/a0119201.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011920/a0119202.png" /> is a natural number. It is essential, in solving several physical and mathematical problems, that each positive rational number is representable as a sum of a finite number of aliquot ratios, with different denominators. Thus, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011920/a0119203.png" />. Aliquot ratios were extensively employed in Ancient Egypt and, as a result, received the name of Egyptian fractions.
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A fraction of the type $1/n$, where $n$ is a natural number. It is essential, in solving several physical and mathematical problems, that each positive rational number is representable as a sum of a finite number of aliquot ratios, with different denominators. Thus, $3/11=1/6+1/11+1/66$. Aliquot ratios were extensively employed in Ancient Egypt and, as a result, received the name of Egyptian fractions.

Revision as of 09:36, 13 April 2014

aliquot fraction

A fraction of the type $1/n$, where $n$ is a natural number. It is essential, in solving several physical and mathematical problems, that each positive rational number is representable as a sum of a finite number of aliquot ratios, with different denominators. Thus, $3/11=1/6+1/11+1/66$. Aliquot ratios were extensively employed in Ancient Egypt and, as a result, received the name of Egyptian fractions.

How to Cite This Entry:
Aliquot ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Aliquot_ratio&oldid=31660
This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article