eli5 Is there a reason that the decimals of pi go on forever (or at least appear to)? Or do it just be like that?

Question

Edit: Thanks for the answers everyone! From what I can gather, pi just do be like that, and other irrational numbers be like that too.

In: 5168

Answer 1

It just so happens that in our universe, squares and circles are incommensurable with each other (they cannot be used to measure each other exactly). If you take the countable integers to represent the length of the sides of a given square, then there will never be a number that can be represented by any combination of countable integers to represent the length of the sides of a corresponding circle which is inscribed within that square (having the same diameter as the side of that square). The ratio between these sides can be approximated as 3.14159…. But if we want to speak about it directly we have to use the term pi and acknowledge that any decimal description of the numbers we are manipulating will be an approximation.

Many other things in our universe are also incommensurable with each other— for example, the distance between two opposite corners of a square is incommensurable with the sides of that square in a different way than the sides of the square and the inscribed circle are. We therefore speak of this ratio as “the square root of two”