Pi and the Egyptians

Date: 05/17/99 at 23:03:01
From: kelly
Subject: Pi

Hi,

I am in need of some help. I already have some background about pi, 
but just need some help with this question. Can you help me?

The Egyptians

The papyrus roll now called the Ahmes Papyrus after an Egyptian scribe 
called Ahmes, who wrote it about 1650 B.C., was discovered in 1858 and 
is now in the British Museum. It contains 84 mathematics problems.

Problem no. 50 involves finding the circle-ratio. Translated into 
today's arithmetic, Ahmes assumes the area of a circular field with a 
diameter of 9 units is the same as the area of a square with sides of 
8 units.

What value for pi in decimals were the Egyptians using?

Date: 05/18/99 at 15:10:43
From: Doctor Rick
Subject: Re: Pi

Hi, Kelly.

Here is a way to figure it out. The area of a circle is

  K = pi * r^2

In the example from the papyrus, the diameter is 9 units, so the 
radius r is 9/2 units. The area K is that of a square with sides 8 
units, so K = 8^2 units. Now we can find pi:

  pi = K / r^2

Plug in the numbers and see what you get. Subtract the true value of 
pi, 3.1415925..., to see how far off the Egyptians were. Is their 
value more or less accurate than 22/7?

Here is a Web site that lists some early values of pi:

  The Precomputer History of Pi (Neal Carothers)
  http://ernie.bgsu.edu/~carother/pi/Pi2.html   

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/