e^(iπ) in 3.14 minutes, using dynamics | DE5

Name: e^(iπ) in 3.14 minutes, using dynamics | DE5
Uploaded: 2019-07-07T14:08:18Z
Duration: 248 s
Description: A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

33Blue1Brown43 videos here

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3.4M views · Jul 7, 2019 · 4:08 · 4 HN recommenders · 4 mentions · discussed 2020–2021

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

Why Hacker News points people here: HN commenters point to it as a quick, visual way to understand Euler's identity.

“3blue1brown explains it better than I could”HN comment, 2020

Recreational & visual math Pure mathematics Explainer #euler's formula #complex numbers #calculus #math visualization #3blue1brown

What Hacker News said 4

Strongly recommendsdavidwfJan 2021

“3Blue1Brown: Amazing math visualizations”

Great first 3Blue1Brown video on how e^pi*i works.

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I keep a Google Document of these to share just in case people ask about my YouTube interests. I Actually Watched All of Them I have actually watched ALL of the videos on these channels and I don’t even feel bad about it :-) I actually like new videos from some of the ones below (like NativLang, for example) but they maybe don’t hold up in the early videos. - Space Time: PBS Physics, sooo good -- link -- Great first video: link - Lindsay Ellis: Really, really intelligent video essays about film and culture -- link -- Great First Video: link - Periodic Videos: Chemistry, including a video for every element -- link -- Great first video (obviously): link Other Math and Science - 3Blue1Brown: Amazing math visualizations -- link -- Great first video, how e^pi*i works: this video - NumberPhile: Fun math videos -- link -- Great first video: link - PBS Eons: Biology! -- link -- Great first video: link - PBS Infinite Series: Math math math, really really hard math -- link -- Great first video: link - SciShow: Science! More poppy but fun -- link -- Silly first show: link -- Actual physics: link - VSauce: Science-y? -- link -- Great first video: link - Practical Engineering: -- link -- Great first video: link Other Humanities - Alliterative: Connections via language -- link -- Great first video about gin and gimlets: link - Bon Appetit: Such fun food stuff! -- Gourmet Makes: link -- It’s Alive: link - Masaman: Genetics and human migration (an

RecommendsdgritskoMay 2020

“is a nice compliment to this post.”

Short visual explanation of Euler's identity.

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3Blue1Brown's video "Understanding e to the i pi in 3.14 minutes" is a nice compliment to this post. this video

RecommendskortexDec 2020

“3blue1brown explains it better than I could”

Geometric understanding of e to the pi i.

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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] this video [3.14 min] link [25 min]

RecommendsadrusiJun 2021

“This video [1] kinda helps, although it glosses over the critical fact”

Builds intuition for Euler's identity, though glosses over rotation by i.

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You actually have to understand calculus for that to actually prove it to you, but, you can show that it seems to work out numerically with a bit of programming knowledge, which I imagine is more common on Hacker News. I don't think either the numerical or symbolic proofs really help build intuition though. This video [1] kinda helps, although it glosses over the critical fact "multiplying by i rotates counterclockwise 90°." [1] this video