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#euler'sformula#grouptheory#3blue1brown

Euler's formula with introductory group theory

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

YouTube
  • Recommended by 3 people: 3 on Hacker News.
  • A classic. People kept recommending it from 2017 to 2024.

Intermediate. Assumes working knowledge.

2.7M views9 years ago3 recommendations

Computer scienceMath for programmersComputation and complexity

An explanation of the intuition behind Euler's formula using the geometric concepts of group theory.

Intuition for e^(πi) = -1, using the main ideas from group theory Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: 3b1b.co/epii-thanks Additional support for this video came from Emerald Cloud Lab: emeraldcloudlab.com/ There's a slight mistake at , 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 Conrad's expository papers: math.uconn.edu/~kconrad/blurbs/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: Filippo ------------------ 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 as an exceptionally clear and intuitive geometric explanation of Euler's formula and group theory.

BucketSorton Hacker News • Recommends

On “Miniatures: Mathematical and Algorithmic Applications of Linear Algebra [pdf]”

That whole channel is amazing! I can start just listing all the videos by virtue of picking out awesome ones, but check out the one he did on Euler's formula1. Blew my mind. 1 link to this video
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kortexon Hacker News • Recommends

On “Alternative notation for exponents, logs and roots? (2011)”

IMHO, the "deeper truth" is addition is translation and multiplication is rotation/stretching (at least when it comes to rings and fields). It involves getting a geometric understanding of e to the pi i, and 3blue1brown explains it better than I could: link 6.28 min link 3.14 min link to this video 25 min
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moefhon Hacker News • Recommends

On “What makes e natural? (2004)”

…teps using f(x+dx)=f(x)+f'(x)*dx, and everything clicked: how exponentials work in the real axis is pretty different from the imaginary axis, but both are completely intuitive and unavoidable once you understand that. Even later I "discovered" the connection with group theory1; that one still blows my mind. 1 This is a really nice explanation: link to this video…
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justifieron Hacker News • Mentions

On “Ask HN: Anyone monetizing their sideproject with direct ads / sponsorships?”

…trimental the current hands off one size fits all ad networks are Some content creators will surely protest 'im a creator stead a salesman' which is a fair complaint but I'd argue 3blue1brown really brings an artistry to the personal ad network the channel is creating.. self curated ads has the potential to be another medium of self expression (o) link to this video .. an aside: the ad that YouTube ran in front of the video I linked when I first clicked on it was offensive and jarring, it depicted an animated Albert Einstein literally scribbling on a black board while a student looked on in dread and three words came in the screen, two of which I can remember 'math ___ sucks' the middle was either: tea…
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l-on Hacker News • Mentions

On “The Fourier Transform, explained in one sentence”

The repeated "many folding", which would be better visualized as tendition, exponentiation pattern also breaks with fractions & at the most basic negative numbers: link to this video
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u/nmarshall23in r/functionalprogramming • Mentions

On “I signed up for Functional programming on my University but math isn't my stront suit, did I make a mistake?”

You would be well served to learn a little group theory. Functional programming can be seen as applied group theory. Also http://learnyouahaskell.com is fun. I learned Haskell, by solving several of the https://projecteuler.net problems.
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