The power tower puzzle | Lockdown math ep. 8

From 3Blue1Brown.

A fun puzzle stemming from repeated exponentiation.
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
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Notes by Ngân Vũ:
https://twitter.com/ThuyNganVu/status/1261014161464516608?s=20

Play along on Desmos:
https://www.desmos.com/calculator/nul32eaaa9

Related videos.
Calculus series:
https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

In particular look at:
https://youtu.be/CfW845LNObM

Numberphile on Grahm’s constant:
https://youtu.be/XTeJ64KD5cg

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Video timeline (thanks to user "noonesperfect")
0:36 Question 1
1:13 Answer 1
1:29 Introduction to tetration
3:37 How exponentiation works in tetration
6:10 Python program for power tower iterations
8:40 Question 2
9:32 Python Program regarding question 2
10:37 Answer 2 and explanation
13:18 Power tower for infinite size converges or not? (Thumbnail question)
15:21 Question 3
16:28 Footage of Grant’s setup arrangement problem due to construction-work back at home.
16:49 Answer 3 and explanation
17:40 Checking logic behind 2 different problems of power towers whose answer converges to the same value (Is it even possible?)
19:42 Checking same logic using Desmos graph tool i.e. Cobweb Graph (Desmos graph link in description)
28:12 Question 4
28:51 Questions from audience tweets
29:15 Knuth’s Up Arrow Notation and Graham’s Number (Check Numberphile video in description)
32:32 Answer 4 and explanation
37:29 Homework/Challenge Puzzle
39:20 Thumbnail question power tower logic
40:55 Audience questions from twitter
41:45 Power tower for complex numbers/Fractal set
45:19 Brainteaser
48:06 More questions from tweets
53:17 Notes for lock-down series in Grant’s Tweeter
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The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

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https://www.3blue1brown.com/faq#manim

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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