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
The first thing to keep in mind is that we as modern humans tend to use base-10 (although that is not always the case), but other bases exist. For example, minutes and seconds are base 60, hours are base 24, and computers work in base 2 (0 and 1).
Pi is defined as the ratio between the circumference and the diameter of a circle. As any number it can be represented in any base, although in different ways. [Here](https://www.virtuescience.com/pi-in-other-bases.html) you can find some examples of pi represented in other numeral systems. So even if you found a special pattern in the digits of pi (in base 10), it wouldn’t be the same in other bases.
That said,
>why and how did we decide or learn that those digits were of pi if it’s an irrational number
we didn’t *decide* those were the digits of pi. Putting aside [some absurd proposal to arbitrarily set a different value to pi](https://en.wikipedia.org/wiki/Indiana_Pi_Bill), once you define a numeral system (base 10? base 60? base 2?), you don’t *decide* the digits of pi. You simply try to *learn* them, to discover them, especially since pi has actually a meaning. It’s not like someone suddenly said “hey, the number 3.1415926…. doesn’t represent anything, but let’s call it pi” or “hey I want to call some number pi. What number? Well, 3.1415926… can do the trick”.
>if it never ends couldn’t you technically just make it up
No. It never ends, so you’ll never be able to compute its *exact* value but that doesn’t mean you can make it up. You can set a threshold where you stop caring, for example after the second or fifth decimal digits, you can approximate, but you can’t make up the *exact* value of pi.
Latest Answers