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

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: [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

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

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] [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] [VIDEO]