\chapter{Numbers and their names.}

\section{What is a number?}

\section{Egyptian fractions}
The Egyptian scribes devised a way to give names to fractional quantities. 
First, they gave names to the unit fraction $\Frac{1}{n}$.  Then they represented
the others as sums of unit fractions.  This was a very clever way to give names to 
fractions, although   it is not immediately clear that every fraction then {\bf has}
such a name.  They did not allow a particular unit fraction to appear more than
once in the name, so  $\Frac{1}{4} + \Frac{1}{4}$ was not an Egyptian fraction.
Unfortunately, there is more than one way to write a particular fraction as an Egytian
fraction (for example, $\Frac{1}{6} + \Frac{1}{3} = \Frac{1}{2}$)
