There is no estimate of the mathematical constant pi (or ) in the Bible. Mathematically-inclined critics sometimes quote I Kings 7:23
And he made a molten sea, ten cubits from the one brim to the other; it was round all about, and his height was five cubits, and a line of thirty cubits compassed it round about.
and point out that since the numbers here are the diamater and ratio of a circle, this implies that whereas is actually a bit more than 3; it’s actually a bit more than 3.14159 which is as far as I can go by memory. After this, they typically add some snarky remark about Biblical accuracy, but the criticism is wrong-headed for two different reasons, either one of which is sufficient to make anyone who spends a second thinking about it realize that the criticism is dumb.
First, this is obviously not a mathematical estimate of . There is no indication here or anywhere else in the literature of the region and period that they even knew that the ratio of diameter to circumference of a circle is a constant; that is, there is no evidence that they knew there was a constant to estimate. What this passage clearly reports is not a mathematical theory, but a pair of measurements, rounded to the nearest cubit.
The entire passage is full of measurements, clearly someone went through the construction site with a measuring line and measured a bunch of stuff while a scribe wrote it all down. The text first specifies the size of the basin by its diameter, implying that they measured the diameter, and then specifically says that they measured the circumference with a line. If you measure the diameter of any circle and it rounds to ten units, then measure the circumference with a measuring line and round to the nearest unit, the most likely result to get is 30 units. That is not an error; it is a rounded value.
Second, people who claim Biblical inerrancy are not claiming high-precision mathematics. If the writer of this report been estimating (which he wasn’t) then his estimate was accurate to within the precision of the report. There is no way to actually write down all of the digits of because there are an infinite number of them. You have to stop somewhere, and there are lots of applications where stopping with 3 works just fine. In other words, even if this were an estimate of , it is not an error; it is just less precise than the critic would like.
I’m not a Biblical literalist, but horrifically bad arguments like that one just annoy me because they reveal that the critic doesn’t really care about the truth, but only about a gotcha.