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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"!)

English
  • Originally Aired May 6, 2023
  • Runtime 27 minutes
  • Production Code ypxKzWi-Bwg
  • Network YouTube
  • Created May 7, 2023 by
    shriek
  • Modified May 7, 2023 by
    shriek