The most educated individuals of ancient civilizations knew that $\pi$ was approximately $3$ or $3$-point something, but there wasn't a high degree of accuracy. That is, of course, until Archimedes Calculated $\pi$.

Archimedes knew how to calculate the perimeter of regular polygons, so first he simply put a square around and inside a circle of radius $1$, giving it a circumference of $2\pi$.

Not a bad start! Just by putting a square outside and inside the circle, he was able to determine that $\pi$ is greater than $2.83$ and smaller than $4$. He simply repeated this process with regular polygons of more sides to get an ever more accurate interval for $\pi$. Genius! This is the interval when you use a regular hexagon:

A lot better! Archimedes was able to continue this process, culminating in a $96$-sided regular polygon! That gave a VERY accurate measurement of $\pi$. He found that...

$$3.14103 < \pi <3.142715$$