Around 250 BC Archimedes found a general algorithm for computing pi to arbitrary accuracy, and used it to prove that 223/71 < π < 22/7. This seems to be when people started using 22/7 as an approximation to pi.
This is a companion discussion topic for the original entry at https://johncarlosbaez.wordpress.com/2025/04/24/civilizational-collapse-part-5/