A new and more circularly proof of a famous infinite product for pi.
Try out Udacity: https://udacity.com/3b1b
Here's supplemental blog post, expanding some of the rigor of this proofs, along with other interesting tidbits about surrounding topics that w...

From 3Blue1Brown

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
Why? Well, people asked, and what better...

From 3Blue1Brown

A most beautiful proof of the Basel problem, using light.
More problem-driven learning: https://brilliant.org/3b1b
Content like this is made possible by the very kind subset of you who choose to contribute for each new video:
https://www.patreon.com/3blu...

From 3Blue1Brown

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...

From 3Blue1Brown

An animated introduction to the Fourier Transform, winding graphs around circles.
Puzzler at the end by Jane Street: https://janestreet.com/3b1b
Funding for these videos comes in large part from viewers, through patreon: https://www.patreon.com/3blue1br...

From 3Blue1Brown

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 an...

From 3Blue1Brown

What's actually happening to a neural network as it learns?
Training data generation + T-shirt at http://3b1b.co/crowdflower
Crowdflower does some cool work and addresses a meaningful need in machine learning, so I was pretty excited that they agreed to ...

From 3Blue1Brown

Subscribe for more (part 3 will be on backpropagation): http://3b1b.co/subscribe
Thanks to everybody supporting on Patreon.
https://www.patreon.com/3blue1brown
http://3b1b.co/nn2-thanks
For any early stage ML startup founders, Amplify Partners would love...

From 3Blue1Brown

Subscribe to stay notified about new videos: http://3b1b.co/subscribe
Support more videos like this on Patreon: https://www.patreon.com/3blue1brown
Special thanks to these supporters: http://3b1b.co/nn1-thanks
For any early-stage ML entrepreneurs, Amplif...

From 3Blue1Brown

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...

From 3Blue1Brown

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...

From 3Blue1Brown

A story of pi, prime numbers, and complex numbers, and how number theory braids them together.
Check out Remix careers: https://www.remix.com/jobs
The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares...

From 3Blue1Brown

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 ...

From 3Blue1Brown

A very quick primer on the second derivative, third derivative, etc.
Full playlist: http://3b1b.co/calculus
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if y...

From 3Blue1Brown

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...

From 3Blue1Brown

What is an integral? How do you think about it?
Check out the Art of Problem Solving: https://aops.com/3blue1brown
Full series: http://3b1b.co/calculus
Series like this one are funded largely by the community, through Patreon, where supporters get ear...

From 3Blue1Brown

Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works.
3Blue1Brown store: http://3b1b.co/store
Let me know what you'd like to see in there.
Full series: http://3b1b.co/calculus
Series like this one are funded largely by the c...

From 3Blue1Brown

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...

From 3Blue1Brown

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...

From 3Blue1Brown

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, whe...

From 3Blue1Brown

A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition.
Check out Brilliant: https://brilliant.org/3b1b
Full series: http://3b1b.co/calculus
Series like this one are funded largely by the com...

From 3Blue1Brown

Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?
Check out the Art of Problem Solving: https://aops.com/3blue1brown
Note, to illustrate my point for...

From 3Blue1Brown

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.
Ful...

From 3Blue1Brown

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...

From 3Blue1Brown

The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful.
Shirts/posters at DFTBA: http://3b1b.co/store
The Great Courses Plus free trial: http://ow.ly/GtbB3083BZc
Mathologer's related video: https://youtu.be/...

From 3Blue1Brown

What fractal dimension is, and how this is the core concept defining what fractals themselves are.
Patreon page: https://www.patreon.com/3blue1brown
Special thanks to the following Patrons: http://3b1b.co/fractals-thanks
Check out Affirm careers here: h...

From 3Blue1Brown

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/3blu...

From 3Blue1Brown

This function 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...

From 3Blue1Brown

After seeing how binary counting can solve the towers of Hanoi puzzle in the last video, here we see how ternary counting solve a constrained version of the puzzle, and how this gives a way to walk through a Sierpinski triangle graph structure.
Thanks to...

From 3Blue1Brown

Binary counting can solve the towers of Hanoi puzzle, and if this isn't surprising enough, it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2).
Thanks to Desmos for their help in supporting this video. ...

From 3Blue1Brown

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 hom...

From 3Blue1Brown

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 math...

From 3Blue1Brown

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 s...

From 3Blue1Brown

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 pro...

From 3Blue1Brown

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 be...

From 3Blue1Brown

For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corres...

From 3Blue1Brown

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 dif...

From 3Blue1Brown

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 geomet...

From 3Blue1Brown

Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through...

From 3Blue1Brown