How was pi discovered?

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.