RebE, you think you got me 🙂 but I am an applied mathematician, not a purist. I can tell you how to get it without writing it down:
1) take a string, make a circle with a radius 1 inch, straighten the string, fold in half, here is your pie
2) draw a right angle triangle with side 1, take the diagonal
What I should have written, precise enough to get the integer number of people at the end precise.
A question now is: did Rav Yohanan put out this calculation on purpose so that answers differ based on precision to trip up those who were bad in math, and make them come back with questions, so that he could indulge in explaining how to approximate pi?!
R Steinsaltz writes (probably not original) that historically there are periods an societies of closed and open science. During closed periods, only selected people have access to knowledge. We had open science when it was all called “philosophy” and maybe in 19th century but it reversed somewhat, as you often need to be a very narrow specialist to understand science (a physicist may not understand some of the biology). We all struggle to understand science and statistics behind a pandemic.