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…

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…

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…

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…

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…

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…

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,…

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…

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…

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…

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,…

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…

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…

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…

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…