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Videos uploaded by user “3Blue1Brown”
How secure is 256 bit security?
 
05:06
Supplement to the cryptocurrency video: How hard is it to find a 256-bit hash just by guessing and checking? What kind of computer would that take? Cryptocurrency video: https://youtu.be/bBC-nXj3Ng4 Thread for Q&A questions: http://3b1b.co/questions Several people have commented about how 2^256 would be the maximum number of attempts, not the average. This depends on the thing being attempted. If it's guessing a private key, you are correct, but for something like guessing which input to a hash function gives a desired output (as in bitcoin mining, for example), which is the kind of thing I had in mind here, 2^256 would indeed be the average number of attempts needed, at least for a true cryptographic hash function. Think of rolling a die until you get a 6, how many rolls do you need to make, on average? Music by Vince 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 809719 3Blue1Brown
Essence of linear algebra preview
 
05:05
This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course. Error corrections: - At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations, when in reality most use CORDIC (or something like it). - Around 30 seconds in, there is a typo in how the determinant is written, which should be ad - bc Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1157155 3Blue1Brown
Fractal charm: Space filling curves
 
02:34
A montage of space filling curves, meant as a supplement to the Hilbert curve video.
Views: 200322 3Blue1Brown
A Curious Pattern Indeed
 
01:49
A teaser for some future videos regarding a pattern which lures an unsuspecting doodler into thinking it will be powers of two.
Views: 385568 3Blue1Brown
The Brachistochrone, with Steven Strogatz
 
16:02
Steven Strogatz and I talk about a famous historical math problem, a clever solution, and a modern twist. ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Patreon: https://www.patreon.com/3blue1brown Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 461289 3Blue1Brown
Vectors, what even are they? | Essence of linear algebra, chapter 1
 
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I imagine many viewers are already familiar with vectors in some context, so this video is intended both as a quick review of vector terminology, as well as a chance to make sure we're all on the same page about how specifically to think about vectors in the context of linear algebra. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1000607 3Blue1Brown
But what *is* a Neural Network? | Deep learning, chapter 1
 
19:13
Subscribe to stay notified about new videos: http://3b1b.co/subscribe Support more videos like this on Patreon: https://www.patreon.com/3blue1brown Or don't. It's your call really, no pressure. Special thanks to these supporters: http://3b1b.co/nn1-thanks Additional funding provided by Amplify Partners. For any early-stage ML entrepreneurs, Amplify would love to hear from you: [email protected] Full playlist: http://3b1b.co/neural-networks Typo correction: At 14:45, the last index on the bias vector is n, when it's supposed to in fact be a k. Thanks for the sharp eyes that caught that! For those who want to learn more, I highly recommend the book by Michael Nielsen introducing neural networks and deep learning: https://goo.gl/Zmczdy There are two neat things about this book. First, it's available for free, so consider joining me in making a donation Nielsen's way if you get something out of it. And second, it's centered around walking through some code and data which you can download yourself, and which covers the same example that I introduce in this video. Yay for active learning! https://github.com/mnielsen/neural-networks-and-deep-learning I also highly recommend Chris Olah's blog: http://colah.github.io/ For more videos, Welch Labs also has some great series on machine learning: https://youtu.be/i8D90DkCLhI https://youtu.be/bxe2T-V8XRs For those of you looking to go *even* deeper, check out the text "Deep Learning" by Goodfellow, Bengio, and Courville. Also, the publication Distill is just utterly beautiful: https://distill.pub/ Lion photo by Kevin Pluck 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 2697099 3Blue1Brown
Snell's law proof using springs
 
03:57
This is a supplement to the Brachistochrone video, proving Snell's law with a clever little argument by Mark Levi.
Views: 92481 3Blue1Brown
The determinant | Essence of linear algebra, chapter 6
 
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The determinant of a linear transformation measures how much areas/volumes change during the transformation. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 630278 3Blue1Brown
Inverse matrices, column space and null space | Essence of linear algebra, chapter 7
 
12:09
How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank and null space, but the computation of those constructs is not discussed. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 495144 3Blue1Brown
But what is the Fourier Transform?  A visual introduction.
 
20:57
An animated introduction to the Fourier Transform, winding graphs around circles. Supported by viewers: https://www.patreon.com/3blue1brown Special thanks to these Patrons: http://3b1b.co/fourier-thanks Follow-on video about the uncertainty principle: https://youtu.be/MBnnXbOM5S4 Puzzler at the end by Jane Street: https://janestreet.com/3b1b 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1717867 3Blue1Brown
Backpropagation calculus | Deep learning, chapter 4
 
10:18
This one is a bit more symbol heavy, and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part 3 of the series, hopefully providing some connection between that video and other texts/code that you come across later. Find the full playlist at http://3b1b.co/neural-networks Thanks to everyone supporting on Patreon. http://3b1b.co/nn3-thanks http://3b1b.co/support For more on backpropagation: http://neuralnetworksanddeeplearning.com/chap2.html https://github.com/mnielsen/neural-networks-and-deep-learning http://colah.github.io/posts/2015-08-Backprop/ 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 videos, subscribe, and click the bell to receive notifications (if you're into that): http://3b1b.co/subscribe If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 408917 3Blue1Brown
Visualizing the Riemann hypothesis and analytic continuation
 
22:11
Understanding the Riemann hypothesis requires understanding a certain function which is famously confusing outside its "domain of convergence", but a certain visualization sheds light on how it extends. There are posters for this visualization of the zeta function at http://3b1b.co/store Thank you to everyone supporting on Patreon: https://www.patreon.com/3blue1brown Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Check out some of Vince's other work here: http://www.vincentrubinetti.com/ For those who want to learn more about complex exponentiation, here are a few resources: - My video on the topic: http://youtu.be/mvmuCPvRoWQ - Mathologer's: https://youtu.be/-dhHrg-KbJ0 - Better Explained: https://goo.gl/z28x2R For those who want to learn more about the relationship between 1+2+3+4+... and -1/12, I'm quite fond of this blog post by Terry Tao: https://goo.gl/XRzyTJ Also, in a different video "What does it feel like to invent math", I give a completely different example of how adding up growing positive numbers can meaningfully give a negative number, so long as you loosen your understanding of what distance should mean for numbers: https://youtu.be/XFDM1ip5HdU Interestingly, that vertical line where the convergent portion of the function appears to abruptly stop corresponds to numbers whose real part is Euler's constant, ~0.577. For those who know what this is, it's kind of fun to puzzle about why this is the case. Special shout-outs to the following Patreon supporters: CrypticSwarm, Ali Yahya, Dave Nicponski, Damion Kistler, Juan Batiz-Benet, Yu Jun, Othman Alikhan, Markus Persson, Joseph John Cox, Luc Ritchie, Shimin Kuang, Einar Wikheim Johansen, Rish Kundalia, Achille Brighton, Kirk Werklund, Ripta Pasay, Felipe Diniz, dim85, Chris , Michael Rabadi, Alexander Juda, Mads Elvheim, Joseph Cutler, Curtis Mitchell, Ari Royce, Bright , Myles Buckley, Andy Petsch, Otavio Good, Karthik T, Steve Muench, Viesulas Sliupas, Steffen Persch, Brendan Shah, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, aidan boneham, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Jeffrey Herman, Jacob Young and Steve Muench. ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1310862 3Blue1Brown
Dot products and duality | Essence of linear algebra, chapter 9
 
14:12
Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 425724 3Blue1Brown
What does genius look like in math?  Where does it come from? (Dandelin spheres)
 
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A beautiful proof of why slicing a cone gives an ellipse. Thoughts on going sponsor-free (for those who missed it): https://www.patreon.com/posts/going-sponsor-19586800 Special thanks: http://3b1b.co/dandelin-thanks New shirts/mugs available: http://3b1b.co/store Video on Feynman's lost lecture: https://youtu.be/xdIjYBtnvZU The 3d animations in the video were done using Grapher, while 2d animations were done using https://github.com/3b1b/manim 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 videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
Views: 423318 3Blue1Brown
Eigenvectors and eigenvalues | Essence of linear algebra, chapter 13
 
17:16
A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Typo: At 12:27, "more that a line full" should be "more than a line full". ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 695867 3Blue1Brown
Derivatives of exponentials | Essence of calculus, chapter 5
 
13:50
What is e? And why are exponentials proportional to their own derivatives? Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following patrons: http://3b1b.co/eoc5-thanks ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 419885 3Blue1Brown
Linear transformations and matrices | Essence of linear algebra, chapter 3
 
10:59
Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 861042 3Blue1Brown
How to count to 1000 on two hands
 
02:34
Typically when we think of counting on two hands, we count up to 10, but fingers can contain much more information than that! This video shows how to think about counting in binary.
Views: 171502 3Blue1Brown
Triangle of Power
 
07:42
In math, exponents, logarithms, and roots all circle around the same idea, but the notation for each varies radically. The triangle of power is an alternate notation, which I find to be absolutely beautiful. (This is the corrected version of the one I put out a month or so ago, in which my animation for all the inverse operations was incorrect) Here's a sketch from the math redditer Cosmologicon showing how this might be usual with practical space considerations: http://i.imgur.com/hAeJokq.jpg This original comes from an answer to a math exchange post by Alex Jordan, which you can find here: http://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots I also briefly flashed a blog post with another interesting alternative for logarithm notation: http://www.solidangl.es/2015/04/a-radical-new-look-for-logarithms.html
Views: 401921 3Blue1Brown
Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2
 
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The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several vectors and adding them together. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 868119 3Blue1Brown
What is backpropagation really doing? | Deep learning, chapter 3
 
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What's actually happening to a neural network as it learns? Next video: https://youtu.be/tIeHLnjs5U8 Training data generation: http://3b1b.co/crowdflower Find the full playlist at http://3b1b.co/neural-networks The following video is sort of an appendix to this one. The main goal with the follow-on video is to show the connection between the visual walkthrough here, and the representation of these "nudges" in terms of partial derivatives that you will find when reading about backpropagation in other resources, like Michael Nielsen's book or Chis Olah's blog. Thanks to everyone supporting on Patreon. http://3b1b.co/nn3-thanks http://3b1b.co/support For more on backpropagation: http://neuralnetworksanddeeplearning.com/chap2.html https://github.com/mnielsen/neural-networks-and-deep-learning http://colah.github.io/posts/2015-08-Backprop/ 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 714051 3Blue1Brown
Ever wonder how Bitcoin (and other cryptocurrencies) actually work?
 
26:21
Bitcoin explained from the viewpoint of inventing your own cryptocurrency. Videos like these made possible by patreon: https://patreon.com/3blue1brown Protocol Labs: https://protocol.ai/ Interested in contributing? https://protocol.ai/join/ Special thanks to the following patrons: http://3b1b.co/btc-thanks Some people have asked if this channel accepts contributions in cryptocurrency form as an alternative to Patreon. As you might guess, the answer is yes :). Here are the relevant addresses: ETH: 0x88Fd7a2e9e0E616a5610B8BE5d5090DC6Bd55c25 BTC: 1DV4dhXEVhGELmDnRppADyMcyZgGHnCNJ BCH: qrr82t07zzq5uqgek422s8wwf953jj25c53lqctlnw LTC: LNPY2HEWv8igGckwKrYPbh9yD28XH3sm32 Supplement video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat Here are a few other resources I'd recommend: Original Bitcoin paper: https://bitcoin.org/bitcoin.pdf Block explorer: https://blockexplorer.com/ Blog post by Michael Nielsen: https://goo.gl/BW1RV3 (This is particularly good for understanding the details of what transactions look like, which is something this video did not cover) Video by CuriousInventor: https://youtu.be/Lx9zgZCMqXE Video by Anders Brownworth: https://youtu.be/_160oMzblY8 Ethereum white paper: https://goo.gl/XXZddT Music by Vince 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 2216835 3Blue1Brown
Change of basis | Essence of linear algebra, chapter 12
 
12:51
How do you translate back and forth between coordinate systems that use different basis vectors? Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support
Views: 319963 3Blue1Brown
Implicit differentiation, what's going on here? | Essence of calculus, chapter 6
 
15:34
Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y). Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc6-thanks ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 348726 3Blue1Brown
Higher order derivatives | Essence of calculus, chapter 10
 
05:39
A very quick primer on the second derivative, third derivative, etc. Full playlist: http://3b1b.co/calculus ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 153040 3Blue1Brown
Who cares about topology?   (Inscribed rectangle problem)
 
18:16
An unsolved conjecture, the inscribed square problem, and a clever topological solution to a weaker version of the question, the inscribed rectangle problem (Proof due to H. Vaughan, 1977), that shows how the torus and Mobius strip naturally arise in mathematical ponderings. Patreon: https://www.patreon.com/3blue1brown Special shout out to the following patrons: Dave Nicponski, Juan Batiz-Benet, Loo Yu Jun, Tom, Othman Alikhan, Markus Persson, Joseph John Cox, Achille Brighton, Kirk Werklund, Luc Ritchie, Ripta Pasay, PatrickJMT , Felipe Diniz, Chris, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, Aidan Boneham, Brent Kennedy, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Ali Yahya, Jeffrey Herman, and Jacob Young ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 837744 3Blue1Brown
Essence of calculus, chapter 1
 
17:05
I want you to feel that you could have invented calculus for yourself, and in this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc1-thanks ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1284730 3Blue1Brown
How pi was almost 6.283185...
 
05:53
Happy pi day! Did you know that in some of his notes, Euler used the symbol pi to represent 6.28..., before the more familiar 3.14... took off as a standard? Plushie creatures now available: http://3b1b.co/store The idea for this video, as well as the live shots, came from Ben Hambrecht, with the writing and animating done by Grant Sanderson. Special thanks to: - University Library Basel, for letting us rummage through their historical collection - Martin Mattmüller from the Bernoulli-Euler center for helpful discussion - Michael Hartl, author of the Tau Manifesto, for pointing us to obscure references - Library of the Institut de France Cinematographer: Eugen Heller 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 397178 3Blue1Brown
Cross products | Essence of linear algebra, Chapter 10
 
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This covers the main geometric intuition behind the 2d and 3d cross products. *Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead. It makes no difference for the result, since the determinant is unchanged after a transpose, but given how I've framed most of this series I think it is more intuitive to go with a column-centric approach. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 305717 3Blue1Brown
Q&A with Grant Sanderson (3blue1brown)
 
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To commemorate crossing 2^20 subscribers, I answer some questions people asked on Reddit. 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 videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
Views: 134103 3Blue1Brown
Music And Measure Theory
 
13:13
A connection between a classical puzzle about rational numbers and what makes music harmonious.
Views: 449881 3Blue1Brown
Fractals are typically not self-similar
 
21:36
What fractal dimension is, and how this is the core concept defining what fractals themselves are. Special thanks to the following Patrons: http://3b1b.co/fractals-thanks Patreon page: https://www.patreon.com/3blue1brown Check out Affirm careers here: http://affirmjobs.3b1b.co Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve, which just so happens to achieve roughness level exactly 2. Slightly rough might be around 1.1-dimension; quite rough could be 1.5; but a very rough curve could get up to 2.0 (or more). A classic example of this is the boundary of the Mandelbrot set. The Sierpinski pyramid also has dimension 2 (try computing it!). The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose "Hausdorff dimension" is greater than its "topological dimension". Hausdorff dimension is similar to the box-counting one I showed in this video, in some sense counting using balls instead of boxes, and it coincides with box-counting dimension in many cases. But it's more general, at the cost of being a bit harder to describe. Topological dimension is something that's always an integer, wherein (loosely speaking) curve-ish things are 1-dimensional, surface-ish things are two-dimensional, etc. For example, a Koch Curve has topological dimension 1, and Hausdorff dimension 1.262. A rough surfaces might have topological dimension 2, but fractal dimension 2.3. And if a curve with topological dimension 1 has a Hausdorff dimension that *happens* to be exactly 2, or 3, or 4, etc., it would be considered a fractal, even though it's fractal dimension is an integer. ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 878360 3Blue1Brown
Divergence and curl:  The language of Maxwell's equations, fluid flow, and more
 
19:59
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 site: https://anvaka.github.io/fieldplay/ 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown
Views: 431689 3Blue1Brown
3blue1brown channel trailer
 
01:32
3blue1brown is a channel animating math. Check out the playlists below for expositions of various neat topics and some clever proofs, and see the "Essence of ______" series for some more student-focussed material. Subscribe to see new videos on this home page in place of this trailer: http://3b1b.co/subscribe
Views: 326839 3Blue1Brown
What they won't teach you in calculus
 
16:23
A visual for derivatives which generalizes more nicely to topics beyond calculus. Supported by viewers: https://www.patreon.com/3blue1brown Problem-driven learning by Brilliant: https://brilliant.org/3b1b Essence of calculus series: http://3b1b.co/calculus Special thanks to the following patrons: http://3b1b.co/alt-calc-thanks 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown
Views: 1252180 3Blue1Brown
Taylor series | Essence of calculus, chapter 11
 
22:20
Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions. Early access to future series: https://patreon.com/3blue1brown Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 623326 3Blue1Brown
What does area have to do with slope? | Essence of calculus, chapter 9
 
12:39
Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc9-thanks ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 265475 3Blue1Brown
Why is pi here?  And why is it squared?  A geometric answer to the Basel problem
 
19:04
A most beautiful proof of the Basel problem, using light. Plushie pi creatures now available: http://3b1b.co/store More problem-driven learning: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Special thanks to patrons: https://www.patreon.com/3blue1brown http://3b1b.co/basel-thanks The content here was based on a paper by Johan Wästlund http://www.math.chalmers.se/~wastlund/Cosmic.pdf Check out Mathologer's video on the many cousins of the Pythagorean theorem: https://youtu.be/p-0SOWbzUYI On the topic of Mathologer, he also has a nice video about the Basel problem: https://youtu.be/yPl64xi_ZZA A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here. https://ggbm.at/yPExUf7b Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details. 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 956002 3Blue1Brown
Gradient descent, how neural networks learn | Deep learning, chapter 2
 
21:01
Subscribe for more (part 3 will be on backpropagation): http://3b1b.co/subscribe Funding provided by Amplify Partners and viewers like you. https://www.patreon.com/3blue1brown http://3b1b.co/nn2-thanks For any early stage ML startup founders, Amplify Partners would love to hear from you via [email protected] To learn more, I highly recommend the book by Michael Nielsen http://neuralnetworksanddeeplearning.com/ The book walks through the code behind the example in these videos, which you can find here: https://github.com/mnielsen/neural-networks-and-deep-learning MNIST database: http://yann.lecun.com/exdb/mnist/ Also check out Chris Olah's blog: http://colah.github.io/ His post on Neural networks and topology is particular beautiful, but honestly all of the stuff there is great. And if you like that, you'll *love* the publications at distill: https://distill.pub/ For more videos, Welch Labs also has some great series on machine learning: https://youtu.be/i8D90DkCLhI https://youtu.be/bxe2T-V8XRs "But I've already voraciously consumed Nielsen's, Olah's and Welch's works", I hear you say. Well well, look at you then. That being the case, I might recommend that you continue on with the book "Deep Learning" by Goodfellow, Bengio, and Courville. Thanks to Lisha Li (@lishali88) for her contributions at the end, and for letting me pick her brain so much about the material. Here are the articles she referenced at the end: https://arxiv.org/abs/1611.03530 https://arxiv.org/abs/1706.05394 https://arxiv.org/abs/1412.0233 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1094036 3Blue1Brown
The more general uncertainty principle, beyond quantum
 
19:21
The Heisenberg uncertainty principle is just one specific example of a much more general, relatable, non-quantum phenomenon. Apply to work at one of my favorite math education companies: http://aops.com/3b1b Special thanks to the following Patrons: http://3b1b.co/uncertainty-thanks You are the ones making this possible: http://3b1b.co/support For more on quantum mechanical wave functions, I highly recommend this video by udiprod: https://youtu.be/p7bzE1E5PMY Minute physics on special relativity: https://youtu.be/1rLWVZVWfdY Main video on the Fourier transform https://youtu.be/spUNpyF58BY Louis de Broglie thesis: http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf More on Doppler radar: Radar basics: https://www.eetimes.com/document.asp?doc_id=1278808 There's a key way in which the description I gave of the trade-off in Doppler radar differs from reality. Since the speed of light is so drastically greater than the speed of things being detected, the Fourier representation for pulse echoes of different objects would almost certainly overlap unless it was played for a very long time. In effect, this is what happens, since one does not send out a single pulse, but a whole bunch of evenly spaced pulses as some pulse repetition frequency (or PRF). This means the Fourier representation of all those pulses together can actually be quite sharp. Assuming a large number of such pulses, it will look like several vertical lines spaced out by the PRF. As long as the pulses are far enough apart that the echoes of multiple objects on the field from different targets don't overlap, it's not a problem for position determinations that the full sequence of pulses occupies such a long duration. However, the trade-off now comes in choosing the right PRF. See the above article for more information. 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 473028 3Blue1Brown
Hilbert's Curve: Is infinite math useful?
 
18:18
Space filling curves, turning visual information into audio information, and the connection between infinite and finite math (this is a reupload of an older video which had much worse audio). Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound, this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/~houde/coleman/sur2.pdf Alternatively, here the NYT summary: https://goo.gl/qNuc14 Also, check out this excellent podcast on Human echolocation: https://goo.gl/23f4Yh For anyone curious to read more about the connections between infinite and finite math, consider this Terry Tao blog post: https://goo.gl/NZ4yrW Lion photo by Kevin Pluck 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brownm/r/3Blue1Brown
Views: 385265 3Blue1Brown
The hardest problem on the hardest test
 
11:15
A difficult geometry puzzle with an elegant solution. Practice more problem-solving at https://brilliant.org/3b1b Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/ Special thanks to the following patrons: http://3b1b.co/putnam-thanks These videos exist thanks to Patreon: https://www.patreon.com/3blue1brown A different write-up of this solution: http://lsusmath.rickmabry.org/psisson/putnam/putnam-web.htm 1992 Putnam with this problem: http://kskedlaya.org/putnam-archive/1992.pdf A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! In the solutions for that problem, by the way, the that Calvin Lin is a friend of mine who works at Brilliant. http://kskedlaya.org/putnam-archive/2005.pdf http://kskedlaya.org/putnam-archive/2005s.pdf 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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 2957119 3Blue1Brown
Three-dimensional linear transformations | Essence of linear algebra, chapter 5
 
04:46
What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 329802 3Blue1Brown
Visualizing the chain rule and product rule | Essence of calculus, chapter 4
 
16:52
A visual explanation of what the chain rule and product rule are, and why they are true. Check out Brilliant: https://brilliant.org/3b1b Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc4-thanks ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 351596 3Blue1Brown
Abstract vector spaces | Essence of linear algebra, chapter 14
 
16:46
The tools of linear algebra are extremely general, applying not just to the familiar vectors that we picture as arrows in space, but to all sorts of mathematical objects, like functions. This generality is captured with the notion of an abstract vector space. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 302384 3Blue1Brown
Tattoos on Math
 
08:15
After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak. One month free audible trial: http://www.audibletrial.com/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 videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 275815 3Blue1Brown
Euler's formula with introductory group theory
 
24:28
How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: - Application software engineer: http://3b1b.co/ecl-app-se - Infrastructure engineer: http://3b1b.co/ecl-infra-se - Lab focused engineer: http://3b1b.co/ecl-lab-se - Scientific computing engineer: http://3b1b.co/ecl-sci-comp Special thanks to the following Patrons: http://3b1b.co/epii-thanks There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 750216 3Blue1Brown
All possible pythagorean triples, visualized
 
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Can we describe all right triangles with whole number side lengths using a nice pattern? Check out Remix careers: https://www.remix.com/jobs Regarding the brief reference to Fermat's Last Theorem, what should be emphasized is that it refers to *positive* integers. You can of course have things like 0^3 + 2^3 = 2^3, or (-3)^3 + 3^3 = 0^3. Special thanks to the following patrons: http://3b1b.co/triples-thanks 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
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What are quaternions, and how do you visualize them?  A story of four dimensions.
 
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How to think about this 4d number system in our 3d space. Thanks to my modern Medicis: https://www.patreon.com/3blue1brown With extra-special thanks here: 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/ 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 videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
Views: 437839 3Blue1Brown