e^(iπ) in 3.14 minutes, using dynamics | DE5
Why Hacker News recommends it
HN commenters point to it as a quick, visual way to understand Euler's identity.
What it is
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.
Recommended by 4 HN commenters across 4 different months, 2020 to 2021.
What Hacker News said
Strong rec davidwf · 2021-01 · on “Ask HN: What YouTube channels do you subscribe to?”
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 - 3Bl
Recommends dgritsko · 2020-05 · on “Why is e^(pi I) = -1?”
3Blue1Brown's video "Understanding e to the i pi in 3.14 minutes" is a nice compliment to this post. [this video]
Recommends kortex · 2020-12 · 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] [this video] [3.14 min] [LINK] [25 min]
Recommends adrusi · 2021-06 · on “Show HN: Kalk, A calculator with math syntax, complex numbers”
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]