# This problem seems hard, then it doesn’t, but it really is

From 3Blue1Brown. The famous (infamous?) Problem 2 on the 2011 IMO Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/windmillthanks You can find data for past IMO results here: https://www.imo-official.org/ The full list of problems considered for the IMO that year, together with their solutions, can be found here: https://www.imo-official.org/problems/IMO2011SL.pdf I made a quick reference…

# Understanding e to the i pi in 3.14 minutes | DE5

From 3Blue1Brown. Euler’s formula intuition from relating velocities to positions. Home page: https://www.3blue1brown.com Yeah yeah, the runtime is 4:08, but it’s 3.14 minutes to the conclusion. Not familiar with the calculus referenced in this video? Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula, from Mathologer: https://youtu.be/-dhHrg-KbJ0 Another perspective from this…

# Pure Fourier series animations for 12 oddly satisfying minutes

From 3Blue1Brown. Because why not? Learn the math behind this: https://youtu.be/r6sGWTCMz2k If you’re curious about the number of vectors used for each animation: – Eighth note: 100 – Sigma: 200 – Britain: 500 – Fourier drawing: 300 – Nail and Gear: 200 – Treble clef: 100 – Hilbert curve: 300 (relatively small given the detail,…

# But what is a Fourier series? From heat flow to circle drawings | DE4

From 3Blue1Brown. Fourier series, from the heat equation to sines to cycles. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de4thanks Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel: https://www.youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ Small correction: at 9:33, all the exponents should have a pi^2 in…

# Solving the heat equation | DE3

From 3Blue1Brown. Boundary conditions, and setup for how Fourier series are useful. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de3thanks More about the heat equation, with a derivation in terms of slope corresponding to heat flow from MIT OCW: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf If you want to learn more about Fourier series, here are a few great…

# But what is a partial differential equation? | DE2

From 3Blue1Brown. The heat equation, as an introductory PDE. Home page: https://www.3blue1brown.com Brought to you by you: 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,…

# Overview of differential equations | DE1

From 3Blue1Brown. How do you study what cannot be solved? Home page: https://3blue1brown.com/ Brought to you by you: 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. Home page: https://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/cramer-thanks Full series: http://3b1b.co/eola —- 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 Brought to you by you: 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. Part 1: https://youtu.be/HEfHFsfGXjs Part 3: https://youtu.be/brU5yLm9DZM Home page: https://www.3blue1brown.com Brought to you by you: 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 Doga Kurkcuoglu: http://bilimneguzellan.net/bouncing-cubes-and-%CF%80-3blue1brown/ And…

# The most unexpected answer to a counting puzzle

From 3Blue1Brown. If this doesn’t blow your mind, I don’t know what will. Part 2: https://youtu.be/jsYwFizhncE Part 3: https://youtu.be/brU5yLm9DZM Brought to you by you: http://3b1b.co/clacks-thanks New to this channel? It’s all about teaching math visually. Take a look and see if there’s anything you’d like to learn. NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/…

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

From 3Blue1Brown. The formula is no mere coincidence. Store: http://3b1b.co/store Home page: https://www.3blue1brown.com Special thanks: http://3b1b.co/sphere-thanks Discussion on Reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as…

# Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces

From 3Blue1Brown. Solving a discrete math puzzle using topology. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/borsuk-thanks 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…

# 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 Brought to you by you: http://3b1b.co/quaternion-explorable-thanks Previous video on Quaternions: https://youtu.be/d4EgbgTm0Bg 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…

# Visualizing quaternions (4d numbers) with stereographic projection

From 3Blue1Brown. How to think about this 4d number system in our 3d space. Brought to you by you: http://3b1b.co/quaternion-thanks Interact with these visuals: http://3imaginary1real.com 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…