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
[Here’s a wiki page](https://en.wikipedia.org/wiki/Chronology_of_computation_of_%CF%80) that you might find interesting: what people have calculated pi to be since about 2000 BCE. 22/7 is actually an approximation that has been in use since Archimedes’ time, and was a world record for accuracy for a while.
But as to your question, the method varies. One of the reasons more accurate calculations of pi are found is because of better calculators (hurray for electric computers), but a bigger reason has been more efficient formulas are found. So to fully answer your question is less ELI5 and more history lesson, which is why I linked the first wiki page.
As a partial answer, first they knew what pi is: the ratio of a circle’s circumference to its diameter. Then they’d use that in combination with other definitions they knew to narrow things down, such as the perimeter of a square will always be bigger than a circle that fits inside it. [Archimedes’ specific example used with a 96 sided shape to get the 22/7 approximation](https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80).
Modern day maths will use polynomials and series, things used often in calculus and thus beyond this answer, but the concept is the same. Starting from the definition of pi, get a formula with a certain answer that will get close to it. And then calculate that formula using as big a number as you can get (like Archimedes’ 96 sided shape being as big a number of sides as he could get).
Latest Answers