4 HN users recommended this explainer4 months2020–2021score 4.5
Years with an HN recommendation, 2007–2026
HN commenters point to it as a quick, visual way to understand Euler's identity.
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.
“3blue1brown explains it better than I could” (HN, 2020)
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
Great first 3Blue1Brown video on how e^pi*i works.
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]
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]
Builds intuition for Euler's identity, though glosses over rotation by i.
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