Laskern, how did you study goyish Math? BTW, FYI I also am somewhat of a mathematician having worked in the actuarial field. In any case, if you look at Rambam’s commentary on the mishna in Eruvin (it’s in the back of most gemarot) you will see that he holds that a convenient estimate is sufficient for halachic matters. 1.4. Interestingly, he knew that pi is irrational although this was not proven until Johann Heinrich Lambert did so in 5521. The Gra points out that the word קו is spelled קוה in the pasuk. קוה divided by קו is extremely close to pi/3.
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