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

e^(iπ) in 3.14 minutes, using dynamics | DE5 on HackerTube: recommended by 4 Hacker News commenters across 4 separate months, 2020–2021.

3Blue1Brown

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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 recommends it

HN commenters point to it as a quick, visual way to understand Euler's identity.

people recommended it
4
separate months
4
strong recommendations
1
discussed on HN
2020–2021
“3blue1brown explains it better than I could”
— kortex, Dec 2020, in “Alternative notation for exponents, logs and roots? (2011)”

What HN commenters said

4 Hacker News comments link this video. Each one links back to its thread.

davidwfJan 2021Strongly recommends

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

in “Ask HN: What YouTube channels do you subscribe to?” · View on HN

adrusiJun 2021Recommends

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

in “Show HN: Kalk, A calculator with math syntax, complex numbers” · View on HN

kortexDec 2020Recommends

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]

in “Alternative notation for exponents, logs and roots? (2011)” · View on HN

dgritskoMay 2020Recommends

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

in “Why is e^(pi I) = -1?” · View on HN

Topics & tags

Recreational & visual mathPure mathematicseuler's formulacomplex numberscalculusmath visualization3blue1brown