3.14159…. so on and so forth, but my question is *why* and *how* did we decide or learn that those digits were of pi if it’s an irrational number? if it never ends couldn’t you technically just make it up? like i saw a news article, a woman/her team calculated TRILLIONS of digits of pi—how is that possible?
In: Mathematics
Pi is defined as the ratio of a circle’s circumference and its diameter. So you can take a circle and you can draw a shape, say a hexagon, around the circle like this:
[https://etc.usf.edu/clipart/43400/43448/6c3_43448_lg.gif](https://etc.usf.edu/clipart/43400/43448/6c3_43448_lg.gif)
The center of the circle and the center of the hexagon are the same. The radius of the circle is therefore also the distance from the center of the hexagon to the midpoint of one of its sides (where it touches the circle). We can also calculate the perimeter of the hexagon, which is more than the perimeter of the circle. We can take the ratio of the perimeter of the hexagon and the radius of the circle and we know we’ll get an answer that’s more than pi.
Similarly, we can draw a hexagon *inside* the circle like this:
[https://etc.usf.edu/clipart/43400/43446/6c_43446_lg.gif](https://etc.usf.edu/clipart/43400/43446/6c_43446_lg.gif)
And do the same thing and get an answer that’s less than pi.
Combine both and we have an upper and lower boundary for pi. We can improve this boundary by doing the same thing with shapes with more sides, as their perimeters will be closer to the circumference of the circle.
Now, this is a very crude and slow way of doing it, but illustrates the principle of how we can nail down a number like pi. Today we have some clever mathematical formulae which have been proven to produce pi, and do so much more quickly than the above method.
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