⬣ 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 ⬣
There’s much to admire about the Golden Ratio, but its significance is largely overblown. In this video, we separate some of the facts from the fiction, while analysing Darren Aronofsky’s “Pi”.
⬣ TIMESTAMPS ⬣
00:00 - Intro
02:57 - What is the Golden Ratio?
04:53 - The Fibonacci Sequence and the Golden Ratio
10:54 - Nature and Diophantine Approximation
15:14 - Hurwitz’s Inequality
21:20 - Numerology and Gematria
26:09 - Is Pi Good?
29:02 - Verdict
⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!
⬣ SEE ALSO ⬣
Numberphile video featuring Ben Sparks:
https://www.youtube.com/watch?v=sj8Sg8qnjOg
Astrology Future Eye
https://astrologyfutureeye.com/numerology/pythagorean-numerology
Assassinations Foretold in Moby Dick! by Brendan McKay
https://users.cecs.anu.edu.au/~bdm/dilugim/moby.html
⬣ REFERENCES ⬣
G. H. Hardy, E. M. Wright: “An Introduction to the Theory of Numbers” Fourth Edition. Oxford University Press (1960).
⬣ CREDITS ⬣
Music by Danijel Zambo, Tobias Voigt, and Apex Music.
Pi (film) footage (C) Protozoa Pictures, Artisan Entertainment, Summit Entertainment.
Requiem for a Dream footage (C) Thousand Words, Protozoa Pictures, Artisan Entertainment, Summit Entertainment.
IMAGES
Gears
https://hips.hearstapps.com/popularmechanics/assets/16/23/1465575513-gears.jpg
Monty Hall
https://en.wikipedia.org/wiki/Monty_Hall_problem#/media/File:Monty_open_door.svg
Golden Spiral
https://www.elegantthemes.com/blog/wp-content/uploads/2019/06/Ratio-768x486.png
Sacred Creation
https://www.sacredgeometryshop.com/sacred-geometry/sacred-geometry-numerology/
Jeeves
https://www.reddit.com/media?url=https%3A%2F%2Fpreview.redd.it%2Fu0v7ecfl8lm51.jpg%3Fauto%3Dwebp%26s%3D8e0cb5aba8041ae18479fb74bf4aef2b12b40b1d
8 Mile poster (C) Universal Pictures
Mona Lisa
https://en.wikipedia.org/wiki/Mona_Lisa#/media/File:Mona_Lisa,_by_Leonardo_da_Vinci,_from_C2RMF_retouched.jpg
Parthenon
https://cdn.hswstatic.com/gif/parthenon-golden-ratio-orig.jpg
Archimedean Spiral
https://en.wikipedia.org/wiki/Archimedean_spiral#/media/File:Archimedean_spiral.svg
Euler Spiral
https://en.wikipedia.org/wiki/Euler_spiral#/media/File:Euler_spiral.svg
Spiral: From the Book of Saw (C) Universal Pictures
Logarithmic Spiral
https://en.wikipedia.org/wiki/Logarithmic_spiral#/media/File:Logarithmic_Spiral_Pylab.svg
Sunflower
https://synchronicitypc.com/wp-content/uploads/2019/08/SunflowerTheScienceExplorer.jpg
Parthenon with Golden Rectangle
https://cdn.shopify.com/s/files/1/0608/0643/0949/files/3_480x480.png?v=1642310689
Pinecone
https://i.pinimg.com/originals/f8/87/52/f88752dc9998062e03266b8631c2ee35.jpg
Pineapple
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSuYQN7eNsFkSWnHWimrA6XhaXl1kNEe8xQmA&s
Adolf Hurwitz
https://upload.wikimedia.org/wikipedia/commons/d/d1/Adolf_Hurwitz.jpg
Nautilus Shell
https://live.staticflickr.com/7233/7351300052_b5135abb54_b.jpg
Milky Way
https://cdn.mos.cms.futurecdn.net/D7AzRK9mDsZnBecvdMhr5Y.jpg
Hurricane Katrina
https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/Katrina_2005-08-28_1700Z.jpg/800px-Katrina_2005-08-28_1700Z.jpg