Meaning of Egyptian fraction | Babel Free

Definitions

1. A representation of a rational number as a sum of distinct unit fractions.
2. A unit fraction.
   rare

Equivalents

Examples

“The fraction #92;frac#123;7#125;#123;10#125; can be written as the Egyptian fraction #92;frac#123;1#125;#123;2#125;#43;#92;frac#123;1#125;#123;5#125;.”

“The calculation of Mᴺ 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 1#47;g#95;1#43;1#47;g#95;2#43;1#47;g#95;3#43;.... Then Mᴺ#61;Mʰ#92;sqrt#91;g#95;1#93;#123;M#125;#92;sqrt#91;g#95;2#93;#123;M#125;#92;sqrt#91;g#95;3#93;#123;M#125;... where each of the roots can be calculated by means of the Newton–Raphson method.”

“1995, C. Pomerance, A. Sárkőzy, Combinatorial number⟳ theory, R. L. Graham, M. Grötschel, L. Lovász (edtors), Handbook of Combinatorics, Elsevier (North-Holland), 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.”

“In [27], Erdős also considers various questions relating to Egyptian fraction decompositions of #92;textstyle 1#61;#92;sumⁿ#95;#123;k#61;1#125;#92;frac#123;1#125;#123;x#95;k#125;.”

“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.”

CEFR level