Afleveringen
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Two colliding blocks compute pi. Here we dig into the physics to explain why.Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gUInstead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comNext video on Grover's Algorithm:https://youtu.be/RQWpF2Gb-gUThe original paper by Gregory Galperin:https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdfAdam Brown's paper on the analogy with Grover's Algorithm:https://arxiv.org/pdf/1912.02207Here's a lovely interactive built by GitHub user prajwalsouza after watching this video: https://prajwalsouza.github.io/Experiments/Colliding-Blocks.htmlMatt Parker's Pi Day video:https://youtu.be/vlUTlbZT4igNY Times blog post about this problem:https://wordplay.blogs.nytimes.com/2014/03/10/pi/Timestamps:0:00 - Intro0:48 - Recap, the surprise pi3:58 - The game plan5:31 - How to analyze the blocks14:59 - The geometry puzzle20:05 - Small angle approximations25:00 - The value of pure puzzlesSEV#7: https://youtu.be/RTCQYcOpmN4The original version of this explanation (now unlisted): https://youtu.be/jsYwFizhncE------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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Qubits, state vectors, and Grover's algorithm for search.Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to share the videos.Home page: https://www.3blue1brown.comAdam Brown's paper on the connection between Grover's Algorithm and block collisions:https://arxiv.org/pdf/1912.02207If you want to learn the relevant underlying quantum mechanics here, a very friendly resource is the course Mithuna at Looking Glass Universe is currently putting together. See, for instance, this explainer of a qubit:https://youtu.be/kgSVkVNxXyUIf you want to learn more about the fundamentals of quantum computing, my friends Michael Nielsen and Andy Matuschak put together this wonderful resource, aimed at ensuring long-term memory of core concepts:https://quantum.country/BBBV Theorem:https://www.scottaaronson.com/qclec/23.pdfTimestamps:0:00 - Misconceptions6:03 - The state vector12:00 - Qubits15:52 - The vibe of quantum algorithms18:38 - Grover’s Algorithm29:30 - Support pitch30:11 - Complex values31:27 - Why square root?34:01 - Connection to block collisions 35:08 - Additional resources------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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Zijn er afleveringen die ontbreken?
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Addressing viewer questions from the last video: https://youtu.be/RQWpF2Gb-gUThese lessons are funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to share the videos.Home page: https://www.3blue1brown.comTimestamps:0:00 - The confusion1:25 - Example: Sudokus7:58 - Linearity14:19 - Is this useful?These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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From the size of the Earth to the size of the universe, the story of how humanity first discovered distances in the cosmos mirrors the history and science.Patreon supporters see early views of new videos: https://www.patreon.com/3blue1brownHome page: https://www.3blue1brown.comTerry has kindly cataloged many of the added nuances, including a few corrections, in this post:https://terrytao.wordpress.com/2025/02/13/cosmic-distance-ladder-video-with-grant-sanderson-3blue1brown-commentary-and-corrections/As an additional correction, the portrait shown for Kepler, despite being somewhat widespread, actually turns out not to be of Kepler. See this article by Václav Pavlík https://ui.adsabs.harvard.edu/abs/2021PhT....74i..10S/abstractAlso, although the Earth is about 4 times as wide as the moon, as it happens, you would not see this with the lunar eclipse composites, since the umbra of Earth's shadow from the sun is sufficiently smaller than the Earth out where the moon is.Artwork by Kurt BrunsThanks to Paul Dancstep for several animations, such as the powers of 10 zoom out and the simulations of shadows on the moon.Moon composite shot by Reddit user _wanderloots: https://www.reddit.com/r/astrophotography/comments/yil0tu/partial_lunar_eclipse_composite/https://youtube.com/@WanderlootsThanks to Tanya Klowden for helpful conversations about the history of the distance ladder.Argument for why if every shadow of a convex shape is a circle, it must be a sphere: https://mathoverflow.net/questions/39127/is-the-sphere-the-only-surface-with-circular-projections-or-can-we-deduce-a-sp------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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Discrete convolutions, from probability to image processing and FFTs.Video on the continuous case: https://youtu.be/IaSGqQa5O-MHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comLive lecture on image convolutions for the MIT Julia labhttps://youtu.be/8rrHTtUzyZALecture on Discrete Fourier Transformshttps://youtu.be/g8RkArhtCc4Reducible video on FFTshttps://youtu.be/h7apO7q16V0Veritasium video on FFTshttps://youtu.be/nmgFG7PUHfoA small correction for the integer multiplication algorithm mentioned at the end. A “straightforward” application of FFT results in a runtime of O(N * log(n) log(log(n)) ). That log(log(n)) term is tiny, but it is only recently in 2019, Harvey and van der Hoeven found an algorithm that removed that log(log(n)) term.Another small correction at 17:00. I describe O(N^2) as meaning "the number of operations needed scales with N^2". However, this is technically what Theta(N^2) would mean. O(N^2) would mean that the number of operations needed is at most constant times N^2, in particular, it includes algorithms whose runtimes don't actually have any N^2 term, but which are bounded by it. The distinction doesn't matter in this case, since there is an explicit N^2 term.These animations are largely made using a custom python library, manim. See the FAQ comments here:https://www.3blue1brown.com/faq#manimMusic by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5uTimestamps0:00 - Where do convolutions show up?2:07 - Add two random variables6:28 - A simple example7:25 - Moving averages8:32 - Image processing13:42 - Measuring runtime14:40 - Polynomial multiplication18:10 - Speeding up with FFTs21:22 - Concluding thoughts
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A visual introduction to probability's most important theoremHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comGalton board shown in the video: https://amzn.to/3ZJK8nYTimestamps0:00 - Introduction1:53 - A simplified Galton Board4:14 - The general idea6:15 - Dice simulations8:55 - The true distributions for sums11:41 - Mean, variance, and standard deviation15:54 - Unpacking the Gaussian formula20:47 - The more elegant formulation25:01 - A concrete example27:10 - Sample means28:10 - Underlying assumptionsCorrection: 6:37 The narration should say "skewed left"Correction: 7:15 Again, the narration should say "skews a tiny bit left"These animations are largely made using a custom python library, manim. See the FAQ comments here:https://www.3blue1brown.com/faq#manimMusic by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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Where's the circle? And how does it relate to where e^(-x^2) comes from?Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comThe artwork in this video is by Kurt Bruns, who used Midjourney as part of the process for some pieces. I wrote more about the specifics of that process and my thoughts around it here: https://www.patreon.com/posts/thoughts-on-ai-83881719Here are several other good posts about the classic Poisson proofvcubingx: https://www.youtube.com/watch?v=9CgOthUUdw4BriTheMathGuy: https://www.youtube.com/watch?v=S79KPrIm_GcDr. Alter's math library: https://idan-alter.github.io/2023/02/20/Gaussian-Integral.htmlAnd if you'd like to see many other variations on approaching this integral, take a look at this expository paper from Keith Conrad: https://kconrad.math.uconn.edu/blurbs/analysis/gaussianintegral.pdfCorrection: 13:46 - The denominator should read 2πσ^2Timestamps:0:00 - The statistician's friend3:44 - The classic proof12:47 - The Herschel-Maxwell derivation21:55 - Reflecting back on the proof23:50 - A bonus problem
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Adding random variables, with connections to the central limit theorem.Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comTimestamps:0:00 - Intro quiz2:24 - Discrete case, diagonal slices6:49 - Discrete case, flip-and-slide8:41 - The discrete formula10:58 - Continuous case, flip-and-slide15:53 - Example with uniform distributions18:42 - Central limit theorem20:50 - Continuous case, diagonal slices25:26 - Returning to the intro quizThese animations are largely made using a custom python library, manim. See the FAQ comments here:https://www.3blue1brown.com/faq#manimMusic by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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Happy Tau Day! Here's something a bit out of the ordinary for you.Thanks to Matt Parker, @standupmaths, for the invite.More about the event: https://festivalofthespokennerd.com/show/an-evening-of-unnecessary-detail/Thanks to Tim Blais, @acapellascience, for helpful thoughts on the song, including the key phrase "How they fool ya"Video about the circle patternhttps://youtu.be/YtkIWDE36qUVideo about those integralshttps://youtu.be/851U557j6HEVideo about the primes in base 4https://youtu.be/jhObLT1LrfoTimestamps:0:00 - Intro1:20 - Song3blue1brown is a channel about animating math, in all senses of the word animate.Website: https://www.3blue1brown.comMailing list: https://3blue1brown.substack.com/Twitter: https://twitter.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownInstagram: https://www.instagram.com/3blue1brownPatreon: https://patreon.com/3blue1brownFacebook: https://www.facebook.com/3blue1brown
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An apparent pattern that breaks, and the reason behind it.Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comTimestamps0:00 - The pattern2:20 - Counting chords4:03 - Counting intersection points6:20 - Euler's characteristic formula11:30 - Connection with Pascal's triangle15:10 - ReflectionsCorrection at 8:56 - The number of the regions should of course be (1, 2, 3, 4, 5), instead of (0,1,2,3,5)These animations are largely made using a custom python library, manim. See the FAQ comments here:https://www.3blue1brown.com/faq#manimMusic by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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A visual trick to compute the sum of two normally distributed variables.Help fund future projects: https://www.patreon.com/3blue1brownHome page: https://www.3blue1brown.comFor the technically curious who want to go deeper, here's a proof of the central limit theorem using Moment generating functions:https://www.cs.toronto.edu/~yuvalf/CLT.pdfAnd here's a nice discussion of methods using entropy:https://mathoverflow.net/questions/182752/central-limit-theorem-via-maximal-entropyCentral limit theoremhttps://youtu.be/zeJD6dqJ5loWhy π is there, and the Herschel-Maxwell derivationhttps://youtu.be/cy8r7WSuT1IConvolutions and adding random variableshttps://youtu.be/IaSGqQa5O-MTimestamps0:00 - Recap on where we are2:10 - What direct calculation would look like3:38 - The visual trick8:27 - How this fits into the Central Limit Theorem12:30 - Mailing listThese animations are largely made using a custom Python library, manim. See the FAQ comments here:https://www.3blue1brown.com/faq#manimMusic by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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The barber pole effect of shining polarized light into sugar water.Next video: https://youtu.be/aXRTczANuIsSteve Mould's video on the topic: https://youtu.be/975r9a7FMqcHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comThanks to Quinn Brodsky for setting up the demo and to the MIT Physics Instructional Resources Lab for their help and materials, especially Josh Wolfe and Caleb Bonyun.These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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Explaining the barber pole effect from the last video: https://youtu.be/QCX62YJCmGkNext video on the index of refraction: https://youtu.be/KTzGBJPuJwMHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comThis Feynman lecture describes this particular approach in more detail:https://www.feynmanlectures.caltech.edu/I_28.htmlTimestamps:0:00 - Recap0:44 - The radiation law6:10 - Simulating the radiation law11:11 - Why the diagonal stripes?16:31 - Why does it twist?These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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How the index of refraction arises, and why it depends on color (as seen with a prism)These lessons are primarily funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comQuotebook Notebooks: https://3b1b.co/storeThis video is largely based on the following Feynmann lecturehttps://www.feynmanlectures.caltech.edu/I_31.htmlLooking Glass Universe videos on the index of refraction:https://youtu.be/uo3ds0FVpXsThe explanation for why the phase of a wave produced by a plane of oscillating charges is a quarter phase behind the wave of a charge in the center of that plane, and hence a quarter phase behind that of a light wave inducing the oscillations, is given in the previous chapter:https://www.feynmanlectures.caltech.edu/I_30.htmlTimestamps:0:00 - The standard explanation3:14 - The plan5:09 - Phase kicks8:25 - What causes light?13:20 - Adding waves16:40 - Modeling the charge oscillation20:59 - The driven harmonic oscillator26:57 - End notesThese animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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Why bending, how can light go "faster" than light, and moreLessons are primarily funded directly by viewers, who get early access to new videos: https://3b1b.co/supportAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comMuch of the last video, as well as this one, is based on the following Feynman Lecture:https://www.feynmanlectures.caltech.edu/I_31.htmlLooking Glass Universe videos on the refractive index:https://youtu.be/uo3ds0FVpXs?si=Q12Rgz9vN1JMo_diTimestamps:0:00 - Why slowing implies bending3:36 - Recap for how slowing happens5:08 - Birefringence6:19 - The barber pole8:20 - When the refractive index is less than 1These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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I had the pleasure of being invited to give Harvey Mudd's commencement speech this year.Reposted here with permission from the UniversityTimestamps:0:00 - End of Harriet Nembhard's introduction0:45 - The cliché2:28 - The shifting goal5:57 - Action precedes motivation7:02 - Timing10:47 - Know your influence12:05 - Anticipate change------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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3d scenes on 2d film, and a diffraction lesson along the way.Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to share the videos.Home page: https://www.3blue1brown.comHologram credits:The Microscope is by Walter Spierings, 1984Donations Hologram by Cherry Optical HolographyLucy in a Tin Hat is by Patrick Keown Boyd, 1988The Star Wars-themed Direct-Write Digital Holograms were produced by Zebra Imaging.The 'Shakespeare' embossed animated integral hologram was made by Applied Holographics.Walter Spierings, who did the microscope, is from Dutch Holographic Laboratory. He wanted me to let you know that anyone should feel free to approach them when it comes to producing holograms, they do a lot of innovative things with the medium: www.holoprint.com Thanks to everyone who helped with this project:Paul Dancstep, for help writing, and for all the 3d modelingCraig Newswanger and Sally Weber, for making the central hologram shownKurt Bruns, for the artwork of Dennis GaborPhoebe Tooke, Wayne Grim, and Rick Danielson, for filming at the exploratoriumQuinn Brodsky and Mithuna Yoganathan, for footage of lasers through diffraction gratingsVince Rubinetti, for writing the musicCliff Stoll for the Klein BottleSmall correction: After the algebra in the end, I say "We don't even make assumptions about R", but that's not quite true. To treat |R^2| as some scaling factor in the expression |R^2| * O, it matters that the amplitude of R is approximately constant around a given point.Gabor's Nobel Prize lecture:https://www.nobelprize.org/uploads/2018/06/gabor-lecture.pdfA few resources we found helpful for this videoSeeing the Light, by Falk, Brill, and Storkhttps://amzn.to/3NgdiqhPractical Holography, by Saxby and Zarcharovashttps://amzn.to/3ZR2MNNPrinciples of Holography by Howard Smithhttps://amzn.to/3ZOihFZTimestamps0:00 - What is a Hologram?3:28 - The recording process11:45 - The simplest hologram17:12 - Diffraction gratings25:15 - Reconstructing the simplest hologram28:24 - Conjugate image31:11 - More complex scenes35:58 - The bigger picture of holography38:27 - The formal explanationSEV1: https://youtu.be/iBYotKfYRQ0These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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A behind-the-scenes look at how I animate videos.Code for all the videos: https://github.com/3b1b/videosManim: https://github.com/3b1b/manimCommunity edition: https://github.com/ManimCommunity/manim/Example scenes shown near the end: https://github.com/3b1b/manim/blob/master/example_scenes.pyI added some more details about the workflow shown in this video to the readme of the videos repo: https://github.com/3b1b/videos?tab=readme-ov-file#workflowThese lessons are funded directly by viewers: https://3b1b.co/supportTimestamp:0:00 - Intro2:39 - Hello World10:32 - Coding up a Lorenz attractor23:46 - Add some tracking points28:52 - The globals().update(locals()) hack32:57 - Final styling on the scene41:42 - Rending the scene44:35 - Adding equations48:43 - Where to startSEV2: https://youtu.be/XEafCqcwBLs------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimhttps://github.com/3b1b/manimhttps://github.com/ManimCommunity/manim/All code for specific videos is visible here:https://github.com/3b1b/videos/The music is by Vincent Rubinetti.https://www.vincentrubinetti.comhttps://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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Geometry puzzles that benefit from shifting the dimension.Bonus video with extra puzzles: https://www.patreon.com/posts/115570453The artwork at the end is by Kurt BrunsThanks to Daniel Kim for sharing the first two puzzles with me. He mentioned the earliest reference he knows for the tile puzzles is David and Tomei's AMM article titled "The problem of Calissons."The idea to include the tetrahedron volume example was based on a conversation with Po Shen Lo about these puzzles, during which he mentioned the case of one dimension lower.I received the cone correction to the proof of Monge's theorem from Akos Zahorsky via email. Also, the Bulgarian team leader Velian Velikov brought up the same argument, and just shot me a message saying "I came across it in a book I found online titled 'Mathematical Puzzles' by Peter Winkler. There, it is attributed to Nathan Bowler"I referenced quaternions at the end, and if you're curious to learn more, here are a few options.This is a nice talk targetted at game developers:https://youtu.be/en2QcehKJd8This video walks through concretely what the computation is for using quaternions to compute 3d rotations: https://youtu.be/-zsnHbQyRncMy own video on the topic is mainly focused on understanding what they do up in four dimensions, which is not strictly necessary for using them, but for math nerds like me may be satisfying:https://youtu.be/d4EgbgTm0BgAlso, one of the coolest projects I've ever done was a collaboration with Ben Eater to make interactive videos based on that topic:https://eater.net/quaternionsTimestamps- 0:00 - Intro- 0:32 - Twirling tiles- 6:45 - Tarski Plank Problem- 10:24 - Monge’s Theorem - 17:26 - 3D Volume, 4D answer- 18:51 - The hypercube stack- 25:52 - The sadness of higher dimensionsSEV#3: https://youtu.be/vXBtyYvMx24------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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The inscribed square/rectangle problem, solved using Möbius strips and Klein bottles.Playlist with more neat proofs: https://www.youtube.com/playlist?list=PLZHQObOWTQDPSKntUcMArGheySM4gL7wSInstead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to simply share the videos.Home page: https://www.3blue1brown.comThis argument was originally by Herbert Vaughan, appearing for examples in this issue of the Topology Proceedings.https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdfThe on-screen argument for why all closed non-orientable surfaces must intersect themselves in 3d is a slight variation on one I heard from Dan Asimov.2020 Paper by Greene and Lobb:https://arxiv.org/pdf/2005.09193Nice Quanta article about this result:https://www.quantamagazine.org/new-geometric-perspective-cracks-old-problem-about-rectangles-20200625/Timestamps:0:00 - Inscribed squares1:00 - Preface to the second edition3:04 - The main surface10:47 - The secret surface16:45 - Klein bottles22:38 - Why are squares harder?25:10 - What is topology?------------------These animations are largely made using a custom Python library, manim. See the FAQ comments here:https://3b1b.co/faq#manimThe music is by Vincent Rubinetti.https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brownhttps://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u------------------3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.Mailing list: https://3blue1brown.substack.comTwitter: https://twitter.com/3blue1brownInstagram: https://www.instagram.com/3blue1brownReddit: https://www.reddit.com/r/3blue1brownFacebook: https://www.facebook.com/3blue1brownPatreon: https://patreon.com/3blue1brownWebsite: https://www.3blue1brown.com
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