View source for Egyptian fraction

==English==
{{wikipedia}}

===Noun===
{{en-noun}}

# {{lb|en|number theory}} A representation of a rational number as a sum of distinct [[unit fraction]]s.
#: {{ux|en|The fraction <math>\frac{7}{10}</math> can be written as the '''Egyptian fraction''' <math>\frac{1}{2}+\frac{1}{5}</math>.}}
#: {{ux|en|The calculation of <math>M^N</math> where both ''M'' and ''N'' are real numbers can be done by expressing ''N'' as the sum of an integer ''h'' and an '''Egyptian fraction''' <math>1/g_1 + 1/g_2 + 1/g_3 + ... </math>. Then <math>M^N = M^h \sqrt[g_1]{M} \sqrt[g_2]{M} \sqrt[g_3]{M} ... </math> where each of the roots can be calculated by means of the {{w|Newton's method|Newton–Raphson method}}.}}
#* '''1995''', C. Pomerance, A. Sárkőzy, ''Combinatorial number theory'', {{w|Ronald Graham|R. L. Graham}}, {{w|Martin Grötschel|M. Grötschel}}, {{w|László Lovász|L. Lovász}} (edtors), ''Handbook of Combinatorics'', Elsevier (North-Holland), [https://books.google.com.au/books?id=5ktBP5vUl5gC&pg=PA1014&dq=%22Egyptian+fraction%22%7C%22Egyptian+fractions%22&hl=en&sa=X&ved=0ahUKEwix7KW43dXbAhUyC6YKHao6DfQQ6AEIjAEwEw#v=onepage&q=%22Egyptian%20fraction%22%7C%22Egyptian%20fractions%22&f=false page 1014],
#*: However, a representation of ''r'' as a sum of distinct '''Egyptian fractions''' is certainly not unique and this fact leads to many questions.
#* {{quote-book|en|year=2013|author={{w|Ronald Graham|R. L. Graham}}|chapter=Paul Erdős and '''Egyptian Fractions'''|editors=László Lovász; Imre Ruzsa; Vera T. Sós|title=Erdős Centennial|publisher=Springer,|pageurl=https://books.google.com.au/books?id=7_zFBAAAQBAJ&pg=PA293&dq=%22Egyptian+fraction%22%7C%22Egyptian+fractions%22&hl=en&sa=X&ved=0ahUKEwix7KW43dXbAhUyC6YKHao6DfQQ6AEIhwEwEg#v=onepage&q=%22Egyptian%20fraction%22%7C%22Egyptian%20fractions%22&f=false|page=293
|passage=In [27], Erdős also considers various questions relating to '''Egyptian fraction''' decompositions of <math>\textstyle 1=\sum^n_{k=1}\frac{1}{x_k}</math>.}}
#* {{quote-book|en|year=2016|author=Annette Imhausen|title=Mathematics in Ancient Egypt: A Contextual History|pageurl=https://books.google.com.au/books?id=IXwkCQAAQBAJ&pg=PA5&dq=%22Egyptian+fraction%22%7C%22Egyptian+fractions%22&hl=en&sa=X&ved=0ahUKEwix7KW43dXbAhUyC6YKHao6DfQQ6AEIbTAO#v=onepage&q=%22Egyptian%20fraction%22%7C%22Egyptian%20fractions%22&f=false|page=5|publisher=w:Princeton University Press
|passage=The modern description of '''Egyptian fraction''' reckoning being "restricted" to unit fractions is obviously anachronistic (indeed, the Egyptian concept of fractions did not include a numerator, but from a historian's point of view this cannot be criticized on the basis that our modern fractions consist of denominator and numerator). Furthermore, this criticism does not do justice to the development of '''Egyptian fractions'''.}}
# {{lb|en|number theory|rare}} A [[unit fraction]].<!--Please leave this as the second definition as its usage in this sense is in the extreme, uttermost minority, and putting it first only adds confusion. - It looks like it is probably wrong anyway - see the rfv page.-->

====Usage notes====
* The term {{m|en|unit fraction}} is more commonly used than '''''Egyptian fraction''''' in the sense with that meaning.

====Translations====
{{trans-top|representation of a rational number as sum of distinct unit fractions}}
* Finnish: {{t|fi|[[egyptiläinen]] [[murtoluku]]}}
{{trans-bottom}}

{{trans-top|unit fraction}}
* Finnish: {{t+|fi|yksikkömurtoluku}}
* Maori: {{t|mi|hautau waetahi}}
{{trans-bottom}}