[llimos]

Actually...

In the original Hebrew version of I Kings, in that verse the word for 'circumference' is traditionally written differently to how it is read (there are instances of this kind of thing all over the Bible [1])

Each letter in Hebrew has a numeric value [2].

As written: קוה = 111

As read: קו = 106

Ratio between them: 111/106 = 1.04717...

Which is exactly the ratio between the reported value of pi (3) and the real value to 4 decimal places (3.1415)

So maybe they did have a better idea than "3". The 3 in the verse is to keep it simple, but there's a clue there for those who want the real number.

[1] https://en.wikipedia.org/wiki/Qere_and_Ketiv

[2] https://en.wikipedia.org/wiki/Gematria