How was pi discovered?

Discussion of the meaning of pi

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 to approximate pi. The Egyptians approximated pi with 256/81.
It is very likely that people 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 always gave the same number, regardless of the size of the circle.

In this sense, we may say that pi was discovered simply by seeing that all circles were similar. Suppose you have two circles, the first a small circle, and the second a bigger circle. Then, enlarging the smaller circle, you 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 they measured large circles. That is why in ancient times, the most frequent approximations of pi were 3, 22/7, or 13/4.

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