vcubingxA visual explanation of one-sentence proof of Fermat's Two Squares Theorem by Don Zagier. Support me on Patreon! patreon.com/vcubingx
This video adapted a lot of material from this paper: arxiv.org/abs/2112.02556 If you're interested in this proof, I highly recommend it and Proofs From The Book! (In general, if you're interested in math, you should read Proofs From The Book)
Some Clarifications: At 9:00, I meant to say 3^2 + 2^2. Sorry :p When it comes to the Zagier Map, one question a friend asked is that we only ever consider cases where the inner square is the smallest square or the largest square - what about the in between cases? To this, try and think of if you can create a windmill with an "in-between" case. If you can/cannot, why? (spoiler you can't!)
A huge thanks to Chaeyeon Lee, Youngjin Park, Oliver Ni, Eric Che and Antonio Kam for helping me review the video!
These animation in this video was made using 3blue1brown's library, manim: github.com/3b1b/manim
Chapters: 0:00 Introduction 1:40 Part 1: The Involution 5:42 Part 2: The Windmill 10:47 Part 3: The Zagier Map 15:12 Putting it all together 17:13 Outro
Is this the most beautiful proof? (Fermats Two Squares)vcubingx2023-12-22 | A visual explanation of one-sentence proof of Fermat's Two Squares Theorem by Don Zagier. Support me on Patreon! patreon.com/vcubingx
This video adapted a lot of material from this paper: arxiv.org/abs/2112.02556 If you're interested in this proof, I highly recommend it and Proofs From The Book! (In general, if you're interested in math, you should read Proofs From The Book)
Some Clarifications: At 9:00, I meant to say 3^2 + 2^2. Sorry :p When it comes to the Zagier Map, one question a friend asked is that we only ever consider cases where the inner square is the smallest square or the largest square - what about the in between cases? To this, try and think of if you can create a windmill with an "in-between" case. If you can/cannot, why? (spoiler you can't!)
A huge thanks to Chaeyeon Lee, Youngjin Park, Oliver Ni, Eric Che and Antonio Kam for helping me review the video!
These animation in this video was made using 3blue1brown's library, manim: github.com/3b1b/manim
Chapters: 0:00 Introduction 1:40 Part 1: The Involution 5:42 Part 2: The Windmill 10:47 Part 3: The Zagier Map 15:12 Putting it all together 17:13 Outro
Music (in order): Philanthrope, mommy - embrace chll.to/7e941f72 GameChops - National Park Philanthrope, Idealism - Still chll.to/a110849c GameChops - Route 113 Helynt - Route 47 Helynt - Bo-omb Battlefield Helynt - Undewater Knowmadic - Faces chll.to/892bc12e Helynt - Littleroot Town
Hope you guys enjoyed the music! I especially had fun picking out the tracks for this video. S/o to Helynt, they make amazing remixes!
The most beautiful proof in math? (Fermat's Two Squares Theorem)
Some tags: number theory, fermat's two squares, windmills, proofs, mathematics, vcubingx v cubingx, vcubing xHow did the Attention Mechanism start an AI frenzy? | LM3vcubingx2024-04-15 | The attention mechanism is well known for its use in Transformers. But where does it come from? It's origins lie in fixing a strange problems of RNNs. Support me on Patreon! patreon.com/vcubingx Language Modeling Playlist: youtube.com/playlist?list=PLyPKqVSnetmELS_I3FRfXZRKAxV5HB9fc&si=IRBpmEtun0xX7X9_
Music (In Order): Philanthrope, mommy - embrace chll.to/7e941f72 Helynt - Hearthome City Helynt - Route 10 GameChops - National Park Helynt - Bo-Omb Battlefield Helynt - Verdanturf Town
Music: Knowmadic - Faces chll.to/892bc12eA one sentence proof?! (Fermats Two Squares)vcubingx2023-12-22 | Watch the full video: youtu.be/r2o11yHAa2UThe secret π in the Mandelbrot Setvcubingx2022-08-06 | Support me on Patreon! patreon.com/vcubingx Offset your carbon footprint on Wren: wren.co/start/vcubingx The first 100 people who sign up will have 10 extra trees planted in their name!
The mandelbrot set is probably the single most iconic picture in all of math. Yet, somehow, someway, there's always something about this fractal that I find myself scratching my head about. Today, let's look at one of those things :)
The unexpected pi hidden in the Mandelbrot Set Some tags: vcubingx, v cubingx, vcubing x, v cubing x, mandelbrot set, pi, fractal,What are Reed-Solomon Codes? How computers recover lost datavcubingx2022-04-09 | An introduction to Modular Arithmetic, Lagrange Interpolation and Reed-Solomon Codes. Sign up for Brilliant! brilliant.org/vcubingx Fund future videos on Patreon! patreon.com/vcubingx
Music, by ChillHop and GameChops (In Order): Mommy x Philanthrope - Embrace GameChops - Route 113 Knowmadic - Faces Idealism - Still GameChops - Azalea Town
Chapters: 0:00 Introduction 2:02 Modular Arithmetic 6:12 Lagrange Interpolation 11:12 Reed-Solomon Codes, Putting it together 14:50 Outro 15:33 Brilliant Ad 16:33 Outro
Tags: Reed-Solomon Codes, Lagrange Interpolation, Finite Field, Error Correcting Codes, Modular Arithmetic, Polynomial Interpolation, Reed Solomon CodesWhat does it mean to take a complex derivative? (visually explained)vcubingx2022-01-07 | The complex derivative, from differentials to the Cauchy-Riemann Equations Support me on Patreon! patreon.com/vcubingx Sign up for Brilliant (sponsored link)! brilliant.org/vcubingx
A huge thanks to @3blue1brown , @Aleph0 , @alfcnz , Sumedh Shenoy, Nikhil Maserang and Oliver Ni for helping me review the video!
If you're interested in learning why conformal doesn't necessarily mean differentiable, read Chapter 4.VI "Conformal = Analytic" of Tristan Needham's "Visual Complex Analysis", which you can find here: http://usf.usfca.edu/vca/
Some extra info: At 20:47, I mention that a function is holomorphic if it satisfies the cauchy-riemann equations. This is not always true, the partial derivatives have to be continuous as well. For example, f(z) = {0 if z=0, z^5/|z^4| if z!=0} satisfies the cauchy-riemann equations but is not differentiable at z=0. Thanks to Ge for pointing this out!
Mistakes: 3:15: The upper number line should still be labeled as "x" instead of "x^2" 14:56 It should be nz^(n-1)
These animation in this video was made using 3blue1brown's library, manim: github.com/3b1b/manim
Chapters: 0:00 Intro 1:53 The Real Derivative, Revisited 4:31 Differential View 9:17 Transformation View 13:02 Conformality 16:01 Cauchy-Riemann Equations 22:15 Brilliant Ad, Stereographic Projection 23:57 Outro, deriv of e^z
What does it mean to take a complex derivative? (visually explained)
Some tags: complex analysis, cauchy-riemann, imaginary, derivative, vcubingxWhat happens *inside* a neural network?vcubingx2021-10-15 | Visuals to demonstrate how a neural network classifies a set of data. Thanks for watching! Support me on Patreon! patreon.com/vcubingx Source Code: github.com/vivek3141/dl-visualization
What does a Neural Network *actually* do? Visualizing Deep Learning, Chapter 2
0:00 Intro 0:18 Recap of Part 1 1:57 Introducing the dataset 2:52 Structure of the Neural Network we’ll be using 3:34 What is softmax? 5:52 Input space decision boundaries 6:24 Modifying the Neural Network to visualize what it’s doing 7:36 Out-of-domain boundaries 8:46 sin(x) as an activation function 9:30 Neuron planes 11:57 Softmax surfaces 13:20 MNIST Transformation 13:42 OutroThe Neural Network, A Visual Introductionvcubingx2020-08-23 | A visual introduction to the structure of an artificial neural network. More to come! Support me on Patreon! patreon.com/vcubingx Source Code: github.com/vivek3141/dl-visualization
This video is an introduction to the calculus of variations. We go over what variational calculus is trying to solve, and derive the Euler-Lagrange equation, the key partial differential equation to all this.
Music by Chillhop: Knowmadic - Faces chll.to/892bc12eThe Coupon Collectors Problemvcubingx2020-04-17 | Get 2 months of skillshare premium here! https://skl.sh/vcubingx
The coupon collector's problem goes as follows: let's say you want to collect N coupons through draws that have an equal probability of getting any of the N coupons. What's the expected value of the number of draws to get all N coupons?
#math #animation #graphsThe Pattern to Prime Numbers?vcubingx2020-01-20 | In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes.
Here's a video on a similar topic by Numberphile if you're interested: youtu.be/uvMGZb0Suyc
There are a few mistakes in this video, so I clarified them in a pinned comment. Sorry about that!
#primes #zeta #mathThe Painters Paradoxvcubingx2019-11-22 | In this video, we talk about the painter's paradox, that describes an object that can't be covered with paint but can be filled with paint. How is it possible to have an object with an infinite surface area but a finite volume? Doesn't it make sense that the outside of an object always takes up less space than the inside?
This video was animated using manim: github.com/3b1b/manim Source code for the animations: github.com/vivek3141/videosThe Divergence Theorem, a visual explanationvcubingx2019-09-02 | This video talks about the divergence theorem, one of the fundamental theorems of multivariable calculus. The divergence theorem relates a flux integral to a triple integral.
This video was animated using manim: github.com/3b1b/manim Source code for the animations: github.com/vivek3141/videosThe Fractional Derivative, what is it? | Introduction to Fractional Calculusvcubingx2019-07-25 | This video explores another branch of calculus, fractional calculus. It talks about the Riemann–Liouville Integral and the Left Riemann–Liouville Fractional Derivative, and ends with an application to the Tautochrone Problem.
------------------ 0:00 Introduction 1:20 Fractional Integration 6:31 The Left R-L Fractional Derivative 11:22 The Tautochrone Problem ----------------------Why does pi show up here? | The Gaussian Integral, explainedvcubingx2019-07-04 | Support me on Patreon! patreon.com/vcubingx Join my discord server! discord.gg/Kj8QUZU
The Gaussian Integral is a term that describes the area under a normal distribution of mean 1. This value is equal to the square root of pi. In this video, I go over the hidden circle behind this, using a bit of multivariable calculus. Hope you enjoy!
This video gives a brief introduction to the line integral. I talk about line integrals over scalar fields and line integrals over vector fields along with a few sample problems.
For some reason, I didn't like this video very much. It doesn't have the satisfying feel I get from some of my other ones. Even though I am extremely satisfied with the animations, I'm not one bit with the audio. I was going to redo it, but then realized I had 550 subs, and decided to upload it anyway, someone might like it.
If you want to study some more, Paul's online notes are great for breezing through the concepts, but if you want a formal course, you could either take it at a college nearby or try Khan/other online classes.
This video was animated using manim: github.com/3b1b/manim Source code for the animations: github.com/vivek3141/videosHow to connect to your Raspberry Pi using Ethernet! (Secure Shell[SSH] and Remote Desktop)vcubingx2017-07-13 | So if you want to ssh or remote desktop to your raspberrry pi, for most people it just doesn't work directly. This video describes how to ssh to your raspberry pi and also remote desktop to your raspberry pi with just one ethernet cable.
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