noun
Meaning 1
A representation of a rational number as a sum of distinct unit fractions.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, number-theory, sciences
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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided