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
Firstly to clarify we didn’t decide the digits of pi, we discovered them in the same way we discovered that the square root of 2 is 1.414213…. . You can calculate pi to a couple of significant figures by constructing a circle (e.g with a compass) and actually measuring the ratio of the diameter to the circumference but this quickly becomes inaccurate.
One step up from that (and the method used for many years) was by drawing polygons (shapes with straight lines) which approximated a circle and working out their areas but again this is very slow and inefficient.
Then around the time of Newton we made some very important discoveries that there were many infinite summations which converged to some multiple of pi.
For example 1 – 1/3 + 1/5 – 1/7 + 1/9 -… = pi/4. This allows you to very quickly calculate pi to many decimal places. As time went on we discovered more series which converged to pi even quicker and using computers sped this up by an incredible amount.
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