History of Fractions

Date: 12/7/95 at 9:30:11
From: Anonymous
Subject: History of Fractions

	I have several math classes coming to our school media center next 
week to research the history of fractions.  The problem is, our media 
center does not have the right resources to help students with their 
assignment.

	They are trying to find out how fractions developed and how they 
have been used in history.

	For example, how did the Babylonians, Ancient Chinese, Egyptians, 
Greeks, or Hindus use fractions?  How were fractions written?  Which 
operations (addition, subtraction, multiplication, division), if any, 
could be carried out with fractions?  How did they expand the use of 
fractions? 

We have a few books that cover what the numerals of these societies 
looked like, but nothing about the history of fractions in ancient 
cultures.  Our public library and our district high school library 
didn't have anything either.

Your help is greatly appreciated!

Date: 3/8/96 at 23:45:47
From: Doctor Jodi
Subject: Re: History of Fractions

Hi there!  If you have access to a web browser, you'll find a detailed 
description of the Babylonian and Egyptian mathematical system, 
including some discussion of fractions, at 

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

Briefly, the Babylonians used base 60, rather than base 10.  Their 
fractional system survives in the hours minutes and seconds notation we 
still use.

The Chinese system is described at

http://aleph0.clarku.edu:80/~djoyce/mathhist/china.html   

Briefly, the Chinese used a symbol for the numbers 1-10, 100, 1000, and 
10000.  2034 would be written 2, 1000, 3, 10, 4 (2 * 1000 + 3*10 +4)

Small bamboo counting rods were used for calculations.  Positions from 
left to right gave place value. Fractions, as far as I can tell from 
this description, were like ours.  You might find a better description 
in the original sources, Development of Mathematics in China and Japan 
(Mikami) and Chinese Mathematics, A Concise History (Li Yan and 
DuShiran).

Some of the resources from the bibliography at 

http://aleph0.clarku.edu:80/~djoyce/mathhist/numerals.html   

may also be useful.

From my understanding of Greek mathematical history, I gather that 
Greeks emphasized the use of ratios.  Euclid's ELEMENTS contains a book 
just on ratios and several others which depend heavily upon it.  You may 
be particularly interested in exploring the golden ratio.

I hope this will give you the information you're looking for.  If you'd 
like more references or don't have access to a web browser, please mail 
us again.

Thanks for your question!

-Doctor Jodi,  The Math Forum