Egyptian fraction

English

Noun

Egyptian fraction (plural Egyptian fractions)

1. (number theory) A representation of a rational number as a sum of distinct unit fractions.
The fraction ${\displaystyle {\frac {7}{10}}}$ can be written as the Egyptian fraction ${\displaystyle {\frac {1}{2}}+{\frac {1}{5}}}$
The calculation of ${\displaystyle M^{N}}$ 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 ${\displaystyle 1/g_{1}+1/g_{2}+1/g_{3}+...}$. Then ${\displaystyle M^{N}=M^{h}{\sqrt[{g_{1}}]{M}}{\sqrt[{g_{2}}]{M}}{\sqrt[{g_{3}}]{M}}...}$ where each of the roots can be calculated by means of the Newton–Raphson method.
2. (number theory, rare) A unit fraction.