How π Emerges From a Forgotten Curve

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⬡ PATREON: Patreon: anotherroof
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⬡ WEBSITE: https://anotherroof.top
⬡ SUBREDDIT: Reddit: anotherroof
⬡ TWITCH: Twitch: anotherroof

⬣ ABOUT ⬣
Happy Halloween! The Leibniz Formula -- the alternating sum of the reciprocals of odd numbers -- converges on π/4. It's a bizarre result. Even more bizarre is the Witch of Agnesi, a curve with a fascinating history. In this video we marry these together, using the Witch to demonstrate why this alternating sum produces π.

This video was sponsored by Brilliant.

⬣ TIMESTAMPS ⬣
00:00 - Introduction
03:37 - Defining the Witch
07:49 - Two Lemmas
11:56 - Witch Area Part I
13:40 - Etymology of the Witch
18:39 - Witch Area Part II
28:55 - Outro

⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!

⬣ REFERENCES ⬣
[1] P. Fermat, Œuvres de Fermat, Methodes de Quadrature, Gauthier-Villars et fils (1891).
[2] G. Grandi, "Note al trattato del Galileo del moto naturale accellerato", Opera Di Galileo Galilei (in Italian), vol. III, Florence p. 393 (1728).
[3] M. Agnesi, Instituzioni analitiche ad uso della gioventú (1748).
[4] J. Colson, Analytical institutions, Wingrave & Rivington (1801).
[5] https://www.smithsonianmag.com/scienc...
[6] D. Struik, A Source Book in Mathematics, Cambridge, Massachusetts: Harvard University Press (1969).
[7] Complete Dictionary of Scientific Biography, Charles Scribner's Sons (Vol. 1.) (2008).
[8] C. Truesdell, Corrections and additions for “Maria Gaetana Agnesi”. Arch. Hist. Exact Sci. 43, 385–386 (1992). https://doi.org/10.1007/BF00374764
[9] P. Fanfani, Vocabolario dell'uso toscano, p. 334 (1863).
[10] S. Stigler, Studies in the History of Probability and Statistics. XXXIII Cauchy and the witch of Agnesi: An historical note on the Cauchy distribution, Biometrika, Volume 61, Issue 2, August 1974, Pages 375–380, https://doi.org/10.1093/biomet/61.2.375
[11] T. F. Mulcrone, The Names of the Curve of Agnesi. American Mathematical Monthly, 64, 359 (1957).
[12] https://www.encyclopedia.com/women/en...

⬣ IMAGE CREDITS ⬣
Cauchy Distribution
https://upload.wikimedia.org/wikipedi...
Soliton
https://commons.wikimedia.org/wiki/Fi...
Witches
https://en.wikipedia.org/wiki/Witch_o...
Implicit Content
https://www.nicepng.com/downpng/u2w7a...
Maria Agnesi
https://upload.wikimedia.org/wikipedi...
Portrait of Fermat by Roland Lefevre, public domain
Portrait of Grandi, public domain.
Clifford Truesdell
https://en.wikipedia.org/wiki/Cliffor...
Pietro Fanfani
https://upload.wikimedia.org/wikipedi...
Jacopone da Todi
https://upload.wikimedia.org/wikipedi...
Gabriel Simeoni
https://upload.wikimedia.org/wikipedi... CREDITS
Cauchy Distribution
https://upload.wikimedia.org/wikipedi...
Soliton
https://commons.wikimedia.org/wiki/Fi...
Witches
https://en.wikipedia.org/wiki/Witch_o...
Implicit Content
https://www.nicepng.com/downpng/u2w7a...
Maria Agnesi
https://upload.wikimedia.org/wikipedi...
Portrait of Fermat by Roland Lefevre, public domain
Portrait of Grandi, public domain.
Clifford Truesdell
https://en.wikipedia.org/wiki/Cliffor...
Pietro Fanfani
https://upload.wikimedia.org/wikipedi...
Jacopone da Todi
https://upload.wikimedia.org/wikipedi...
Gabriel Simeoni
https://upload.wikimedia.org/wikipedi...

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