Following the old Greeks, we can try approaching π by instead of having a circle, having
regular polygons with increasing number of sides.
Superimposed on a circle:
The perimeter of the inside polygon will always be less than that of the circle.
The perimeter of the outer polygon will always be greater than that of the circle.
By dividing the mean of the two polygon perimeters by the diagonal of the circle we can approach π.
The more sides our polygons have, the closer will our result be to the actual value of π.
Play with this below (circle radius r = 1):
Number of sides (3 ≤ n ≤ 50):
Inner polygon
Circle
6.282
2.000
3.141
Outer polygon
Mean (polygons)
Estimation of π with increasing number of polygon sides (n)