The more sides a polygon has, the closer it gets to the circle
In the 3rd century BC, when there were no calculators, Archimedes drew a regular polygon that fit exactly inside a circle and another regular polygon that exactly enclosed it. He proved that pi must lie somewhere between the two. Increase the number of sides and see it for yourself.
How it works: The perimeter of a regular n-gon drawn inside a circle is always smaller than the circle's circumference, while the perimeter of a regular n-gon drawn outside the circle is always larger. So the ratios "inner polygon perimeter ÷ diameter" and "outer polygon perimeter ÷ diameter" trap pi between them. As n increases, this range gets narrower and narrower.