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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Archimedes found a way back in ancient Greece. He was big on geometry and trigonometry.
Let’s say you have a regular polygon inscribed in a circle. (This means that every corner of the polygon touches the edge of the circle.) If you know the radius of the circle and the area of the polygon, you can do some trig to get the area of the regular polygon with twice as many sides inscribed in the circle.
So we can start with a hexagon. It’s easy to get the area of a hexagon. Then we can use the trig formula to get the area of the 12-sided polygon inscribed in the circle. Then we can do it again to get the area of the 24-sided polygon. Then 48-sided, 96-sided and so on as far as we want.
A polygon with that many sides is really close to a circle. Like, you’d have to look really close to even see the difference. So pi is really close to the area that you calculated for the polygon. But you can go as far as you want, approximating pi as well as you want.
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