And a classic thing in the kuzari, he talks about the length of the lunar month in jewish tradition, about being a really really accurately transmitted tradition going back to king david.
29 days 12 hours 793 chalakim (a very accurate approximation)
that`s
29 days 12 hours 44 minutes 3 and a third of a second.
If you look at that in days 29.xxxxxx it is accurate to 4dp.
the western world did not get it that accurate until NASA sent tools up there.. (then got it even more accurate. But we use the tradition even though we know it is an approximation, same with pi).
I am not sure if the babylonians had it that accurate, I don`t think they did. I did have a book by dr jeffrey satinover that listed all the ancient peoples, and they did not have it that accurate..
of course, it is possible that peoples used the calculation we have via jewish tradition. Some Jews had a background in astronomy because of experience with the jewish lunar calendar..
That is impressive. ... But wouldn't we get more than just four decimal places if or more accurate pi if we were given this knowledge in prophesy? Just wondering that.
note- it was not in prophesy, it was transmitted by sinai... That doesn't change anything, But anyhow..
Since the torah's purpose is not to transmit mathematics, we would only need/use an approximation.
Infact, for example, in halacha, I think we use Pi=3 , which is of course an approximation. But it is what we use even if we have it more accurately. (I think the RAMBAM says that.. And I think the written torah has a calculation that uses it as 3)
I am not sure the purpose of such an exact measure of a lunar month is. Even as accurate as we have it (within a second!). Since we count months in complete days.
Maybe in the days pre fixed(automated) calendar. the sanhedrin used it somehow to check that the testimony of the witnesses was consistent with what is possible astronomically/mathematically.
Or maybe hillel made use of it to make the fixed(automated) calendar. Over many years a difference between solar and lunar builds up, so an accurate figure for the month, is important for making predictions decades or hundreds of years in the future.