How can I make an experiment where you find the relationship between diamater and area of a circle?
The relationship being π(0.5d)^2

I was thinking getting a few circular items, placing them graphing paper, trace the circles, and count the approximate amount of squares within the circle.
But how will this get the person doing the experiment to finding π(0.5d)^2 ???

Question

How can I make an experiment where you find the relationship between diamater and area of a circle?
The relationship being π(0.5d)^2

I was thinking getting a few circular items, placing them graphing paper, trace the circles, and count the approximate amount of squares within the circle.
But how will this get the person doing the experiment to finding π(0.5d)^2 ???

anonymous · Answer

How about draw n-gons outside of the circle, and the same n-gon on the inside of the circle, with increasing number of n, until you achieve a close enough number to pi, which will then get you a ratio with the diameter, which you can calculate with respect to the polygons that you drew both inside and outside the circle?