Egyptian Fraction

Date: 3/29/96 at 17:35:31
From: Don Coleman
Subject: Egyptians

Dear Dr. Math,
Annie Farretti, a fifth grade student at Meadowthorpe Elementary
School in Lexington, Kentucky, has asked me a question that I
cannot answer. Can you?

Why did the Egyptians use a special symbol for the fraction 2/3?

(See Burton's "History of Mathematics", Wm. C. Brown (1995), p. 37.
ISBN 0-697-16089-0)

I could make guesses such as "It came up so often that they
made up a new symbol," and other made-up reasons, but she
would like to have something that sounds a bit more scholarly.
I hope you can help her. If you can, I will pass it along to
her. 

Thanks

Don Coleman 
Mathematics Dept, University of Kentucky, Lexington, KY

Date: 4/1/96 at 2:22:57
From: Doctor Jodi
Subject: Re: Egyptians

Hi there Don! This sounds like a great question.  The St. Andrew's 
math history site has some information on Babylonian and Egyptian 
Mathematics at 

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_and_Egyptian.html   

The site includes references to a few books on this topic:

References: 

    1. A Aaboe, Episodes from the Early History of Mathematics (1964). 
    2. R J Gillings, Mathematics in the Time of the Pharaohs  
       (Cambridge, MA., 1982). 
    3. G J Toomer, Mathematics and Astronomy, in J R Harris (ed.), 
       The Legacy of Egypt (Oxford, 1971), 27-54. 
    4. O Neugebauer and A Sachs, Mathematical Cuneiform Texts 
       (New Haven, CT., 1945). 
    5. A B Chace, L S Bull, H P Manning and R C Archibald, The 
       Rhind Mathematical Papyrus (Oberlin, Ohio, 1927-29). 
    6. J Hoyrup, Babylonian mathematics, in I Grattan-Guinness (ed.), 
       Companion Encyclopedia of the History and Philosophy of the 
       Mathematical Sciences (London, 1994), 21-29. 
    7. C S Roero, Egyptian mathematics, in I Grattan-Guinness (ed.), 
       Companion Encyclopedia of the History and Philosophy of the 
       Mathematical Sciences (London, 1994), 30-45. 
    8. J Friberg, Methods and traditions of Babylonian mathematics. 
       Plimpton 322, Pythagorean triples, and the Babylonian triangle 
       parameter equations, Historia Mathematica 8 (1981), 277-318. 

Unfortunately, I don't have access to a mathematical library right now 
(since I'm in Chile) but perhaps you can find the answer in one of 
these books.

Let us know what you find out!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/