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#pi#primenumbers#complexnumbers

Pi hiding in prime regularities

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

YouTube
  • Recommended by 3 people: 3 on Hacker News.
  • Presented by Grant Sanderson, creator of 3Blue1Brown

Intermediate. Assumes working knowledge.

2.8M views9 years ago3 recommendations

Computer scienceMath for programmersComputation and complexityCryptography

Grant Sanderson explains how pi emerges from prime numbers using complex numbers, sums of squares, and number theory.

A story of pi, primes, complex numbers, and how number theory braids them together. Mathologer on why 4k + 1primes break down as sums of squares: youtu.be/DjI1NICfjOk Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: 3b1b.co/leibniz-thanks Home page: 3blue1brown.com/ For those of you curious about the finer details, here's a write-up from the viewer Daniel Flores justifying the final approximation: danielfloresmath.github.io/notes/pi-hiding-in-prime-regulari… The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as "Fermat's theorem on sums of two squares": goo.gl/EdhaN2 Music by Vince Rubinetti: vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Timestamps - Introduction - Counting lattice points - Gaussian integers - The lattice point recipe - Counting on one ring - Exploiting prime regularity - Combining the rings - Branches of number theory Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 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: 3b1b.co/recommended Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3Blue1Brown Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown Reddit: reddit.com/r/3Blue1Brown

Why it's here

3 people recommend this

What people say. Recommended for its beautiful and intuitive visual proof connecting complex numbers, primes, and pi.

pqhon Hacker News • Recommends

On “The Exterior Algebra and Central Notions in Mathematics (2015) [pdf]”

This is a really beautiful proof that connects complex numbers and primes to derive a formula for calculating pi. It should only require high-school algebra prereqs. link to this video If you want to truly follow the proof, there's one little bit on the chi function in there which is connected to something called the One Sentence Proof. This looks rather esoteric and takes a bit of pondering to wrap your head around, but again only really requires high-school level algebra. Doing proofs like this is what math is really about. This is how you come to really understand. And this video also happens to be entertaining in how well-put-together it is.
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zerbon Hacker News • Recommends

On “Physics Travel Guide: a tool that makes learning physics easier”

…roofs, shows you the intuition behind fields of math, and constructs subjects in such a way as to make you feel like you could have invented them yourself. You'll still need a good textbook or something to go with the videos, but they cement the understanding in your mind very well and even open the door to more formal proofs. My favorite video is link to this video . You'll have to take an additional step to get a complete proof (hint: read and work through the One Sentence Proof), but this is a beautiful piece of mathematics, shown in an understandable manner.…
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throwawaymathon Hacker News • Recommends

On “Mathematicians Seal Loophole to Breaking RSA Encryption”

This is a half hour 3Blue1Brown video: link to this video If you're willing to watch at least the first half of it, I think it'll give you a very intuitive grounding for 1) why integers have unique polynomial representations, and 2) why that's related to (semi)prime factorization.
View on Hacker News