A tale of civilizational decline and rebirth.
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.
By the Middle Ages, math had backslid so much in Western Europe that even scholars believed that pi was actually equal to 22/7.
Around 1020, a mathematician named Franco of Liège got interested in the ancient Greek problem of squaring the circle. But since he believed that π is 22/7, he started studying the square root of 22/7. 🙄
There's a big difference between being misinformed and being stupid. Liège was misinformed but not stupid. He went ahead to prove that the square root of 22/7 is irrational!
The proof resembles the old Greek proof that the square root of 2 is irrational. I don't know if Liège was aware of that. I also don't know if he noticed that if pi were 22/7, it *would* be possible to square the circle with straightedge and compass. I also don't know if he wondered *why* pi was 22/7. He may have just taken it on authority.
But still, a noble effort.
Liège was a student of a student of the famous scholar Gerbert of Aurillac (~950–1003) who studied in the Islamic schools of Sevilla and Córdoba and thus got some benefits of a culture whose mathematics was light years ahead of Western Europe. Gerbert wrote something interesting: he said that the benefit of mathematics lie in the "sharpening of the mind".
I got most of this interesting tale from the book "3000 Years of Analysis", which turns out to be quite fun to read. It's over 700 pages long, but you can start anywhere!
https://mathscholar.org/2019/02/simple-proofs-archimedes-calculation-of-pi/
John Carlos Baez /
npub17u…8pd6m
2025-04-24 17:57:10
Author Public Key
npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6mPublished at
2025-04-24 17:57:10Event JSON
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"content": "A tale of civilizational decline and rebirth. \n\nAround 250 BC Archimedes found a general algorithm for computing pi to arbitrary accuracy, and used it to prove that 223/71 \u003c π \u003c 22/7. This seems to be when people started using 22/7 as an approximation to pi.\n\nBy the Middle Ages, math had backslid so much in Western Europe that even scholars believed that pi was actually equal to 22/7. \n\nAround 1020, a mathematician named Franco of Liège got interested in the ancient Greek problem of squaring the circle. But since he believed that π is 22/7, he started studying the square root of 22/7. 🙄 \n\nThere's a big difference between being misinformed and being stupid. Liège was misinformed but not stupid. He went ahead to prove that the square root of 22/7 is irrational!\n\nThe proof resembles the old Greek proof that the square root of 2 is irrational. I don't know if Liège was aware of that. I also don't know if he noticed that if pi were 22/7, it *would* be possible to square the circle with straightedge and compass. I also don't know if he wondered *why* pi was 22/7. He may have just taken it on authority.\n\nBut still, a noble effort.\n\nLiège was a student of a student of the famous scholar Gerbert of Aurillac (~950–1003) who studied in the Islamic schools of Sevilla and Córdoba and thus got some benefits of a culture whose mathematics was light years ahead of Western Europe. Gerbert wrote something interesting: he said that the benefit of mathematics lie in the \"sharpening of the mind\".\n\nI got most of this interesting tale from the book \"3000 Years of Analysis\", which turns out to be quite fun to read. It's over 700 pages long, but you can start anywhere! \n\nhttps://mathscholar.org/2019/02/simple-proofs-archimedes-calculation-of-pi/",
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