```From:           don@cam.ov.com (Donald T. Davis)
Newsgroups:     sci.math
Subject:        Re: Egyptian Fractions
Date:           12 Nov 1996 12:07:00 -0500
Organization:   ....
```

```Le Compte de Beaudrap <jd@cpsc.ucalgary.ca> writes:
>
> what is an Egyptian Fraction?

egyptian scribes did arithmetic calculations in a
seemingly bizarre way. when they had to handle a
fractional quantity, they represented it as a sum
of an integer and several "unit fractions," each of
the form 1/n. so, for example, they handled 4 5/6
as 4 + 1/2 + 1/3.  fractions with big denominators
were very cumbersome in this system, and both addition
and multiplication of fractional quantities required
a lot of table-lookup, so as to reduce 2/n terms to
standardized sums of distinct 1/m terms.

no-one knows why the egyptians found this style
necessary; it may be that they just couldn't conceive
of a better way, or that they found it more practical
for the problems that they had to solve. in their
defense, we should remember that our modern "better
ways" seem obvious to us now, but 8,000 years ago,
none of this was obvious; these people invented a lot
of what we now take for granted as "civilization."

it does seem, though, that the mental gymnastics
necessary to handle egyptian arithmetic was part
of what informed both greek number mysticism, and
the early number theory that grew out of it. for
example, the notion of a "perfect number," which
is equal to the sum of its divisors, now seems
silly and useless, but perfect numbers were of
great practical importance in working with egyptian
fractions.

-don davis, boston
```