New lessons Tuesdays and Friday, noon pacific time.

OVERSEAS

自然ログが「自然」である理由は何ですか? |エピソード7 ロックダウンのライブ数学

Intro to the geometry complex numbers.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1258219199769440257

Errors:
- On the first sketch of a complex plane, there is a "2i" written instead of "-2i".
- At the end, in writing the angle sum identity, the last term should be sin(beta) instead of sin(alpha).
- During Q9, the terms in parentheses should include an i, (1/2 + sqrt(3)/2 i)

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

The graphing calculator used here is Desmos.
https://www.desmos.com/

The "Complex slide rule" came from Geogebra, via Ben Sparks.
https://www.geogebra.org/m/mbhbdvkr

Curious about other animations?
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.

------------------
Video Timeline (thanks to user "Just TIEriffic")
0:00:30 - W3 Results
0:01:00 - W4 Prompt
0:02:00 - Ask What would you call 'imaginary numbers'?
0:06:40 - Startingpoint & assumptions
0:10:25 - W4 Results
0:11:25 - Q1 Prompt
0:12:20 - Q1 Process
0:14:05 - RotatingCoordinates
0:16:40 - Q1 Result
0:17:40 - Q2
0:18:15 - Q3 Prompt
0:19:40 - Q3 Results
0:21:35 - RotationAnimation
0:22:35 - 3 facts about Multiplication
0:25:40 - Q4 Prompt
0:26:10 - Ask imaginary I vs physics i&j
0:28:15 - Q4 Result
0:31:00 - GeoGebraDemo
0:32:10 - Q5 Prompt
0:33:30 - Q5 Results
0:34:00 - Q5 Solution
0:35:55 - RotatingImages Example
0:37:10 - PythonExample
0:38:25 - PythonImage Rotation Example
0:40:35 - Ask Vectors & Matrices for rotation
0:42:40 - Q6 Prompt
0:46:55 - Q6 Results
0:47:25 - Q6 Solution
0:52:20 - RedefiningAngle Addition
0:57:20 - Q7 Prompt
0:57:55 - Ask Can we do without complex numbers?
1:00:10 - Q7 Results
1:00:55 - Q7 Solution
1:05:45 - Q8 Prompt
1:06:30 - Ask sum/difference of angles
1:09:25 - Q8 Results
1:10:25 - Q8 Solution
1:12:00 - DesmosExample
1:15:05 - Bringing it all together
1:16:25 - The "cis" shorthand explained
1:18:05 - Q9 Prompt
1:19:35 - Q9 Results
1:20:55 - ClosingRemarks
------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

複素数の基礎 |エピソード3 ロックダウンのライブ数学

Compound interest, e, and how it relates to circles.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Great Mathologer video:
   • e to the pi i for dummies  

Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1258221677990703105
https://twitter.com/ThuyNganVu/status/1258222002889875457

My other videos on imaginary exponents:
   • e^(iπ) in 3.14 minutes, using dynamic...  
   • Euler's formula with introductory gro...  

Mistakes:
In the off-handed remarks on quaternions, I mentioned rotation in 4d would require 10 degrees of freedom.  That's wrong, what I should have said was it requires 6 degrees of freedom, and rotation in 5D is what requires 10 degrees of freedom.

------------------
Video Timeline (Thanks to user "Just TIEriffic")
0:00:00 Welcome
0:00:55 Q1: Prompt (Would you take an imaginary interest rate)
0:02:05 "e to the pi i for dummies" video shoutout
0:02:45 Q1: Results
0:03:30 Q2: Prompt (two banks, two rates)
0:04:55 Ask: Beauty of connections in math
0:06:00 Q2: Results
0:07:05 Desmos for Q2
0:09:10 Q3: Prompt (savings growth rate, 6% every 6mo)
0:10:35 Q3: Results
0:12:35 Desmos graph explored
0:14:45 Breaking down an interest rate
0:18:00 An interesting interest equation
0:19:20 Q4: Prompt (100*(1+0.12/n)^2 as n → ∞)
0:21:05 Ask: Quaternions
0:22:35 Q4: Results
0:24:50 Explaining Q4
0:26:40 Defining e
0:28:40 The definition of e from previous lectures
0:30:45 The imaginary interest rate
0:32:35 Graphing this relationship
0:33:50 The imaginary interest rate animation
0:37:55 Compounding continuously with i
0:40:45 The spring & Hooke's law
0:43:20 Q5: Prompt (Δx & Δv for a spring)
0:44:50 Ask: Rotation in for multiple dimensions
0:47:45 Q5: Results
0:49:50 Rewriting the spring's position
0:55:00 Bringing it all together
0:59:00 Ask: Hints on last lecture's homework
1:03:25 Closing Remarks
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

仮想金利 |エピソード5 ロックダウンのライブ数学

Another view on the quadratic formula.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1258217451323416577

Po Shen Loh on quadratics:
   • A Different Way to Solve Quadratic Eq...  

Welch Labs on imaginary numbers:
   • Imaginary Numbers are Real  

Mistakes (there will always be mistakes):
At minute 22, I write "b' / 2" instead of "-b' / 2".

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
0:00 - Introduction
2:56 - "How often am I going to use this?" + ray tracing example
5:38 - Mental math tricks (factoring numbers, differences of squares)
13:36 - Properties of quadratic functions
18:40 - Deriving the variant quadratic formula
23:07 - Practice problems (ft. complex numbers!)
34:10 - Deriving the traditional quadratic formula from the variant
41:07 - Conclusion (key takeaways)
43:21 - Fun with joke poll questions
------------------

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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

より単純な二次公式 |エピソード1 ロックダウンのライブ数学

Tips on problem-solving, with examples from geometry, trig, and probability.
Past episodes with integrated quizzes: https://itempool.com/c/3b1b
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks
Huge huge thanks to Ben Eater:    / eaterbc  
And Cam Christensen, creator of ItemPool: https://itempool.com/

Notes by Ngân Vũ:
https://twitter.com/ThuyNganVu/status/1265480770832855040

Mistakes:
50:35, there should be a dx in the integral
54:40, if you notice the mistake here and are inclined to complain, keep watching


Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
Video timeline (thanks to user "noonesperfect")
0:34  9-Problem Solving Principles/Tip 
1:15  Question 1 (Probability)
2:08  Who is Ben Eater? 
4:25  Inscribed angle theorem, θL=2*θs
5:58  Tip-1
7:48  Tip-2
8:16  Question 2
9:34  Answer 2 
10:29 Tip-3
15:17 Tip-4
22:48 Question 3
25:56 Answer 3 (Marked incorrectly, Answer: Option D) 
26:31 Answer 1
27:28 Explanation for Q1, Floor function
30:38 Tip-5
32:53 Tip-6
33:36 Question 4
34:43 Answer 4
36:37 Question 5
38:10 Answer 5
41:48 Probability graph in Desmos 
44:08 Revisiting an alternating series sum for ln(2)
47:29 Tip-7
51:08 Tip-8
55:23 Audience questions through tweets
57:28 Tip-9
58:29 Python programming for various probability question
1:04:31 Arts created using Desmos graph tool with mathematical expressions
1:05:54 Thank you, appreciation to the team and all. 
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

Tips to be a better problem solver [Last live lecture] | Ep. 10 Lockdown live math

What does it mean to compute e^{pi i}?
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1258220129327800320
https://twitter.com/ThuyNganVu/status/1258220541686628353

Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really converge, what they converge to, and how exactly you define a product with infinitely many terms. For anyone curious about the technical details, what you would want to show is that the Cauchy Product of the series for exp(x) and exp(y) converges to the product of the values exp(x) and exp(y) for any particular x and y. That requires the Merten's Theorem.

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
Video Timeline (Thanks to user "Just TIEriffic")
0:00:00 Welcome
0:00:20 Ending Animation Preview
0:01:15 Reminders from previous lecture
0:03:30 Q1: Prompt (Relationship with e^iθ=…)
0:05:40 Q1: Results
0:07:15 WTF, Whats The Function
0:10:00 Exploring exp(x)
0:11:45 Exploring exp(x) in Python
0:14:45 Important exp(x) property
0:15:55 Q2: Prompt (Given f(a+b) = f(a)f(b)…)
0:17:30 Ask: Which is more interesting, special cases or the general case
0:20:00 Q2: Results
0:23:50 Will a zero break Q2?
0:25:40 The e^x convention
0:27:10 Q3: Prompt (i^2 = -1, i^n = -1)
0:27:45 Ask: Zero does not break Q2
0:30:20 Q3: Results
0:31:05 Comparison to Rotation
0:33:00 Visualizing this relationship
0:36:50 The special case of π
0:39:20 Periodic nature of this relationship
0:39:40 Q4: Prompt (e^3i)
0:41:35 Q4: Results
0:43:55 Explaining the celebrity equation
0:45:55 Homework / Things to think about
0:49:15 Ask: Zero does break Q2.
0:50:30 Closing Remarks
------------------

The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

オイラーの公式は実際には何を言っているのでしょうか? |エピソード4 ロックダウンのライブ数学

Back to the basics with logarithms.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Triangle of power:
   • Triangle of Power  

Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1258222677573001219

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

対数の基礎 |エピソード6 ロックダウンのライブ数学

A fun puzzle stemming from repeated exponentiation.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

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:
   • Essence of calculus  

In particular look at:
   • The other way to visualize derivative...  

Numberphile on Grahm's constant:
   • Graham's Number - Numberphile  

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
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 
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

パワータワーパズル |エピソード8 ロックダウンのライブ数学

i^i, visualized and explained.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Mistakes:
At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct.  It's what we'd think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i) is.

Beautiful notes by Ngân Vũ 
https://twitter.com/ThuyNganVu/status/1263522876403011585

Video by Matt Parker:
   • What does i^i = ?  

Video by Red Pen Black Pen
   • i^i  

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
Video timeline (thanks to user "nooonesperfect")

0:18  Exponential function for i^i
1:26  Question 1
2:27  Plug-in imaginary number in exp(x) polynomial
3:38  Answer 1 and explanation
7:35  What it really means i^i?
9:14  e^it as a position vector 
11:30 Question 2
12:39 Audience question from twitter
13:14 Answer 2
14:52 Where you get after traveling π/2 units of time for position vector e^it
19:48 Question 3
20:42 Audience tweets
23:34 Answer 3
35:50 Question 4
37:11 Answer 4
40:11 How exp(rx) or b^x really works?
46:28 Question 5
47:49 Audience tweets
49:26 Answer 5
57:06 Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number
1:06:06 Questions to think about
1:08:51 Audience tweets 
1:09:09 Power tower for i 
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

Curious about other animations?
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.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

i の i 乗に対する直観 |エピソード9 ロックダウンのライブ数学

Intro to trig with a lurking mystery about cos(x)^2
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com/
Brought to you by you: https://3b1b.co/ldm-thanks

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

-----------------

Contents:
Introduction  - 0:00
Q1 Graph of (cos θ)²  - 2:14
Q2 Translations of cos θ to (cos θ)²  - 5:34
Q3 f(2x) = f(x)²  - 10:54
Intro to Trig  - 13:14
Q4 sin(3) & cos(3)  - 16:44
SohCahToa - 20:44
Q5 Leaning Tower  - 22:29
How to Compute Trig Functions?  - 30:59
Q6 sin(π/6)  - 33:34
Q7 cos(π/6)  - 36:19
Q8 Trig of -θ  - 43:34
Computing Trig Functions  - 47:44
Q9 cos(π/12)  - 0:49:54
Adv Trig Functions  - 0:56:44
Q10 Graph of tan(θ)  - 1:00:30
JSON comment  - 1:02:24
“The most exciting part of the lecture” –1:05:34

------------------

The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/

The graphing calculator used here is Desmos.
https://www.desmos.com/

Curious about other animations?
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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3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com/
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

Lockdown math