# But what is a partial differential equation? | Overview of differential equations, chapter 2

From 3Blue1Brown. The heat equation, as an introductory PDE. Home page: https://www.3blue1brown.com Thanks to these supporters: http://3b1b.co/de2thanks Infinite powers, by Steven Strogatz: https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Universe/dp/1328879984 Typo corrections: – At 1:33, it should be “Black-Scholes” – At 16:21 it should read “scratch an itch”. If anyone asks, I purposefully leave at least one typo in each video, like…

# Overview of differential equations | Chapter 1

From 3Blue1Brown. How do you study what cannot be solved? Home page: https://3blue1brown.com/ Special thanks to these supporters: http://3b1b.co/de1thanks Need to brush up on calculus? https://youtu.be/WUvTyaaNkzM Error correction: At 6:27, the upper equation should have g/L instead of L/g. Steven Strogatz NYT article on the math of love: https://opinionator.blogs.nytimes.com/2009/05/26/guest-column-loves-me-loves-me-not-do-the-math/ Interactive visualization of the example from…

# Cramer’s rule, explained geometrically | Essence of linear algebra, chapter 12

From 3Blue1Brown. This rule seems random to many students, but it has a beautiful reason for being true. Full series: http://3b1b.co/eola Home page: https://www.3blue1brown.com/ Special thanks to these supporters: http://3b1b.co/cramer-thanks —- If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can…

# How colliding blocks act like a beam of light…to compute pi.

From 3Blue1Brown. The third and final part of the block collision sequence. Part 1: https://youtu.be/HEfHFsfGXjs Part 2: https://youtu.be/jsYwFizhncE Home page: https://www.3blue1brown.com Special thanks to these supporters: http://3b1b.co/clacks-thanks Error correction: I wrote the answer as floor(pi/theta), when really it should be ceiling(pi/theta) – 1 t account for values of theta perfectly dividing pi. For example, the…

# So why do colliding blocks compute pi?

From 3Blue1Brown. Solution to previous block collision puzzle: https://youtu.be/HEfHFsfGXjs Part 3: https://youtu.be/brU5yLm9DZM Home page: https://www.3blue1brown.com Special thanks to these viewers: http://3b1b.co/clacks-thanks Many of you shared solutions, attempts, and simulations with me this last week. I loved it! Y’all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By…

# The most unexpected answer to a counting puzzle

From 3Blue1Brown. If the answer here doesn’t blow your mind, I don’t know what will. Part 2: https://youtu.be/jsYwFizhncE Part 3: https://youtu.be/brU5yLm9DZM Home page: https://www.3blue1brown.com Stay tuned for more: http://3b1b.co/subscribe Special thanks to these supporters: http://3b1b.co/clacks-thanks https://www.patreon.com/3blue1brown *Spoiler alerts!* NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ The original paper by Gregory Galperin: https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf Evidently, Numberphile…

# But WHY is a sphere’s surface area four times its shadow?

From 3Blue1Brown. Two lovely ways of relating a sphere’s surface area to a circle. Home page: https://www.3blue1brown.com Fourier socks, pi plushies, and more: http://3b1b.co/store Happy holidays! Discuss on reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ 3blue1brown is predominantly supported via Patreon: https://www.patreon.com/3blue1brown With special thanks to these members: http://3b1b.co/sphere-thanks The first proof goes back to Greek times, due to Archimedes,…

# Sneaky Topology (The Borsuk-Ulam theorem)

From 3Blue1Brown. Solving a discrete math puzzle using topology. Home page: https://www.3blue1brown.com Want more fair division math fun? Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) These videos are supported by the community. https://www.patreon.com/3blue1brown The original 1986 by Alon and West with this proof https://m.tau.ac.il/~nogaa/PDFS/Publications/The%20Borsuk-Ulam%20Theorem%20and%20bisection%20of%20necklaces.pdf VSauce on fixed points https://youtu.be/csInNn6pfT4 EE Paper using…

# What DO we know about turbulence?

From 3Blue1Brown. Here we look at some of the order amidst chaos in turbulence. Vortex rings with Physics Girl: https://youtu.be/N7d_RWyOv20 Home page: https://www.3blue1brown.com Special thanks to these supporters: http://3b1b.co/turbulence-thanks https://patreon.com/3blue1brown Thanks to Dan Walsh for many great ideas, and thanks to Mike Hansen for many helpful conversations. Error correction: I meant to describe Kolmogorov as…

# Quaternions and 3d rotation, explained interactively

From 3Blue1Brown. Go experience the explorable videos: https://eater.net/quaternions Ben Eater’s channel: https://www.youtube.com/user/eaterbc Previous video on Quaternions: https://youtu.be/d4EgbgTm0Bg Special thanks to these supporters: http://3b1b.co/quaternion-explorable-thanks Nice explanation of Gimbal Lock: https://youtu.be/zc8b2Jo7mno Great videos comparing Euler angles and quaternions, from the perspective of an animator: https://youtu.be/syQnn_xuB8U https://youtu.be/4mXL751ko0w Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown —————— 3blue1brown is a channel about…

# What are quaternions, and how do you visualize them? A story of four dimensions.

From 3Blue1Brown. How to think about this 4d number system in our 3d space. Home page: https://www.3blue1brown.com Thanks to supporters: http://3b1b.co/quaternion-thanks Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland: https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ If you want to contribute translated subtitles or to help review those that have already been made by others and need approval,…

# Q&A with Grant Sanderson (3blue1brown)

From 3Blue1Brown. To commemorate crossing 2^20 subscribers. FAQ from home page: https://www.3blue1brown.com/faq Subreddit: https://www.reddit.com/r/3blue1brown AMC problem shown on screen: https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_12A_Problems/Problem_22 Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown —————— 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…

# Ever wondered why slicing a cone gives an ellipse? It’s wonderfully clever!

From 3Blue1Brown. Dandelin spheres, conic sections, and a view of genius in math. Home page: https://www.3blue1brown.com Special thanks: http://3b1b.co/dandelin-thanks Thoughts on the recent change to be sponsor-free: https://www.patreon.com/posts/going-sponsor-19586800 Video on Feynman’s lost lecture: https://youtu.be/xdIjYBtnvZU I originally saw the proof of this video when I was reading Paul Lockhart’s “Measurement”, which I highly recommend to all…

# 3b1b featured creators #1

From 3Blue1Brown. Think Twice: https://www.youtube.com/channel/UC9yt3wz-6j19RwD5m5f6HSg LeiosOS: https://www.youtube.com/user/LeiosOS Welch Labs: https://www.youtube.com/user/Taylorns34 Infinity plus one: https://infinityplusonemath.wordpress.com/ Check out the ones on relativity! https://infinityplusonemath.wordpress.com/2017/03/11/a-mathematical-intro-to-special-relativity/ Music by Enoch Kim https://soundcloud.com/themusemaker —————— 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…

# Divergence and curl: The language of Maxwell’s equations, fluid flow, and more

From 3Blue1Brown. Intuitions for divergence and curl, and where they come up in physics. Thoughts on going sponsor-free: https://www.patreon.com/posts/19586800 Special thanks to these supporters: http://3b1b.co/divcurl-thanks My former work on divergence and curl at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you’ll really enjoy this…