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

From 3Blue1Brown. Tips on problem-solving, with examples from geometry, trig, and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks —————— 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…

Intuition for i to the power i | Lockdown math ep. 9

From 3Blue1Brown. i^i, visualized, and explained. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/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)…

Does contact tracing necessarily sacrifice privacy? (via Nicky Case)

From 3Blue1Brown. Though many contact tracing apps involve location tracking, they don’t have to. Help spread the message: https://3b1b.co/tweet-ctracing Or share it on Facebook: https://3b1b.co/fb-ctracing Original post by Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting his work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where…

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 Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/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: 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 —————— The live question setup with stats on-screen is…

What makes the natural log “natural”? | Lockdown math ep. 7

From 3Blue1Brown. All about ln(x). Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At 16:00, the sum should be written with a "…" to indicate going to infinity. At 38:41, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.…

Logarithm Fundamentals | Lockdown math ep. 6

From 3Blue1Brown. Back to the basics with logarithms. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 —————— 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…

Imaginary interest rates | Lockdown math ep. 5

From 3Blue1Brown. Compound interest, e, and how it relates to circles. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes: In the off-handed remarks on quaternions, I mentioned rotation in 4d would…

What is Euler’s formula actually saying? | Lockdown math ep. 4

From 3Blue1Brown. What does it mean to compute e^{pi i}? Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258220129327800320 https://twitter.com/ThuyNganVu/status/1258220541686628353 —————— 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…

Complex number fundamentals | Lockdown math ep. 3

From 3Blue1Brown. Intro to the geometry complex numbers. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/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…

Trigonometry fundamentals | Lockdown math ep. 2

From 3Blue1Brown. Intro to trig with a lurking mystery about cos(x)^2 Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks —————– 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)  –…

The simpler quadratic formula | Lockdown math ep. 1

From 3Blue1Brown. Another view on the quadratic formula. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watch?v=ZBalWWHYFQc Welch Labs on imaginary numbers: https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF Mistakes (there will always be mistakes): At 22:00, I write "b’ / 2" instead of "-b’ /…

Lockdown math announcement

From 3Blue1Brown. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Innumerable thanks to Ben Eater for helping behind the scenes here: https://www.youtube.com/user/eaterbc —————— 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…

Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

From 3Blue1Brown. An introduction to probability density functions Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/thanks Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always great Terence Tao. https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf Also, for the real analysis buffs among you,…

Simulating an epidemic

From 3Blue1Brown. Experiments with toy SIR models Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/sir-thanks Awesome fan-made interactives: https://prajwalsouza.github.io/Experiments/Epidemic-Simulation.html https://learningsim.itch.io/pandemic-spread-simulation Simulations by Harry Stevens at the Washington Post: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/ Simulations by Kevin Simler at Melting Asphalt: https://meltingasphalt.com/interactive/outbreak/ Excellent visualization of each country’s current growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watch?v=54XLXg4fYsc Another good interactive to…

Binomial distributions | Probabilities of probabilities, part 1

From 3Blue1Brown. Part 2: https://youtu.be/ZA4JkHKZM50 Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/beta1-thanks John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/ —————— These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it’s not the most well-documented tool, and it has…

Exponential growth and epidemics

From 3Blue1Brown. A good time for a primer on exponential and logistic growth, no? Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/covid-thanks Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watch?v=54XLXg4fYsc Data source: https://www.worldometers.info/coronavirus/coronavirus-cases/#case-tot-outchina Some have (quite rightfully) commented on how you shouldn’t look at the R^2 of linear regressions…