Ok, pi is probably a bit over the head of your average 5 year old. I know the definition of pi is circumference / diameter, but is that really how we get all the digits of pi? We just get a circle, measure it and calculate? Or is there some other formula or something that we use to calculate the however many known digits of pi there are?
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Pi is always an approximation. Before Newton came up with some calculus to calculate it, the Greeks did it in a way that is easier to explain.
To approximate pi, you take a circle and cut it into four pie slices – so you have four 90 degree angles forming four triangles where the length of the far side is approximately a fourth of the circles diameter. We can calculate that length by using the Pythagorean theorem. So radius squared + radius squared ~= (circumference x .25) squared. To make it a more accurate calculation, cut the circle into more pie slices. The more pie slices you use, the more digits and more accurate approximation of pie you get.
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