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⬣ LINKS ⬣
⬡ PATREON: https://www.patreon.com/anotherroof
⬡ CHANNEL: https://www.youtube.com/c/AnotherRoof
⬡ WEBSITE: https://anotherroof.top
⬡ SUBREDDIT: https://www.reddit.com/r/anotherroof
⬡ TWITCH: https://www.twitch.tv/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/science-nature/18th-century-lady-mathematician-who-changed-how-calculus-was-taught-180969078/
[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/encyclopedias-almanacs-transcripts-and-maps/agnesi-maria-gaetana-1718-1799
⬣ IMAGE CREDITS ⬣
Cauchy Distribution
https://upload.wikimedia.org/wikipedia/commons/4/47/CauchyVerteilung.PNG
Soliton
https://commons.wikimedia.org/wiki/File:Soliton_hydro.jpg
Witches
https://en.wikipedia.org/wiki/Witch_of_Agnesi#/media/File:Witch_of_Agnesi_curves.svg
Implicit Content
https://www.nicepng.com/downpng/u2w7a9e6w7e6i1u2_parental-advisory-implicit-content/
Maria Agnesi
https://upload.wikimedia.org/wikipedia/commons/5/57/Maria_Gaetana_Agnesi.jpg
Portrait of Fermat by Roland Lefevre, public domain
Portrait of Grandi, public domain.
Clifford Truesdell
https://en.wikipedia.org/wiki/Clifford_Truesdell#/media/File:Clifford_Truesdell.jpg
Pietro Fanfani
https://upload.wikimedia.org/wikipedia/commons/4/4c/Pietro_Fanfani.jpg
Jacopone da Todi
https://upload.wikimedia.org/wikipedia/commons/0/0c/Paolo_Uccello_040.jpg
Gabriel Simeoni
https://upload.wikimedia.org/wikipedia/commons/f/f0/Gabriel_Simeoni.pngIMAGE CREDITS
Cauchy Distribution
https://upload.wikimedia.org/wikipedia/commons/4/47/CauchyVerteilung.PNG
Soliton
https://commons.wikimedia.org/wiki/File:Soliton_hydro.jpg
Witches
https://en.wikipedia.org/wiki/Witch_of_Agnesi#/media/File:Witch_of_Agnesi_curves.svg
Implicit Content
https://www.nicepng.com/downpng/u2w7a9e6w7e6i1u2_parental-advisory-implicit-content/
Maria Agnesi
https://upload.wikimedia.org/wikipedia/commons/5/57/Maria_Gaetana_Agnesi.jpg
Portrait of Fermat by Roland Lefevre, public domain
Portrait of Grandi, public domain.
Clifford Truesdell
https://en.wikipedia.org/wiki/Clifford_Truesdell#/media/File:Clifford_Truesdell.jpg
Pietro Fanfani
https://upload.wikimedia.org/wikipedia/commons/4/4c/Pietro_Fanfani.jpg
Jacopone da Todi
https://upload.wikimedia.org/wikipedia/commons/0/0c/Paolo_Uccello_040.jpg
Gabriel Simeoni
https://upload.wikimedia.org/wikipedia/commons/f/f0/Gabriel_Simeoni.png
⬣ MUSIC CREDITS ⬣
"Night Watch" by Torus.
"Playfully" by V Draganov.
"Ursula Bones" by Roger Gabalda.
"Haunted House" by Danijel Zambo.
"Graveyard Tango" by Oliver Massa.
"Fairytales" by Danijel Zambo.
"Cautious Optimism" by Apex Music.
"The Air we Breathe" by Apex Music.
"Hostage" by Richard Bodgers.