From:don@cam.ov.com (Donald T. Davis)Newsgroups:sci.mathSubject:Re: Egyptian FractionsDate:12 Nov 1996 12:07:00 -0500Organization:....

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