Powell’s Pi Paradox: the genius 14th century Indian solution
Around 1400 there lived an Indian astronomer and mathematician by the name of Madhava of Saṅgamagrāma. He was the greatest mathematician of his time and, among other mathematical feats, he and his followers managed to discover a lot of calculus 200 years before Newton and Leibniz did their thing. While preparing a video about this Indian calculus it occurred to me that some of Madhava’s discoveries can be used to give a nice intuitive explanation of Powell’s Pi Paradox, a very counterintuitive property of the famous Leibniz formula
π/4=1–1/3 1/5–1/7 1/9–...
that Martin Powell stumbled upon in 1983. In the end, giving an introduction to Madhava’s discoveries and giving that intuitive explanation is what I ended up doing in this video. (“Leibniz formula“ should really be “Madhava formula“!)
00:00 Intro
00:35 Powell’s Piradox :)
04:08 Calculus made in India
15:18 Explanation of the paradox using Madhava’s correction terms
1 view
110
20
1 year ago 00:27:29 1
Powell’s Pi Paradox: the genius 14th century Indian solution
1 year ago 01:37:08 1
“2032 wird das Währungssystem zusammenbrechen!“ - Martin Armstrong