Re: how was pi discovered?

Hello Rob!

Nobody knows how pi was discovered.  We do know that pi has been known
for over  4000 years.

In 2000 BC the Babylonians used 3 1/4 as an approximation to pi, and the
Egyptians used 256/81.

It is very likely that people of thousands of years ago observed that 
circles
of
different sizes were similar.  If you  measure the circumference of any 
circle
and divide it by the diameter of the same circle, you will get the number 
pi.

It is very easy to think that mathematicians of thousands of years ago would
have noticed that circumference divided by diameter would always give the
same number, regardless of the size of the circle.

In this sense we may say that pi was discovered by simply seeing that all
circles were similar.  Suppose you have two circles, the first a small 
circle, and the second a bigger circle.  Then if you have a way to make the 
smaller
circle bigger, you can turn it into exactly the bigger circle.

But once it was noticed that pi existed, how was it calculated.  How did the
ancients know how big pi was?

We think that they simply measured large circles.  That is why in ancient
times the most frequently approximations of pi have been 3, or 22/7 or 13/4.

None of these of course are exactly pi.  Pi cannot be written exactly except
by naming it.  When we write the name pi, we are specifying exactly the
value of pi.  When we write 3.14 we are specifying only an approximation to
pi.

Kermit Rose
kermit@polaris.net