Eli5: I always thought pi is 22/7, but recently i found out that 22/7 is a number that is pretty close to pi, not pi itself. Then how do mathematicians found more “pi” ?

Question

Eli5: I always thought pi is 22/7, but recently i found out that 22/7 is a number that is pretty close to pi, not pi itself. Then how do mathematicians found more “pi” ?

In: 167

Answer 1

There are several techniques. The most simple to understand mathematically is probably calculating perimeters of inscribed and circumscribed polygons of a unit circle.
The perimeter of a unit circle is 2(pi). You can get the formula for a side of a regular polygon easy enough, and calculate the perimeters of the inscribed and circumscribed polygons. Start with a square and double the number of sides for each successive calculation, and the upper bound and lower bound quickly converge to 2(pi).