e^(iπ) in 3.14 minutes, using dynamics | DE5
3Blue1Brown4 HN recommenders · recommended in 4 months, 2020–2021
explainer · intro · evergreen · 2020–2021 on HN
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.
HN commenters point to it as a quick, visual way to understand Euler's identity.
Up next
3 mo on HNEuler's formula with introductory group theory
3Blue1Brown
3 HN recommender · 2017–2024
2 mo on HNMOLTEN GLASS VS Prince Rupert's Drop - Smarter Every Day 285
SmarterEveryDay
2 HN recommender · 2023–2023
3 mo on HNHyperbolica: A Non-Euclidean Adventure [Old Trailer]
CodeParade
3 HN recommender · 2021–2023
3 mo on HNMicrotonal Guitar (Fixed Fret) - Tolgahan Çoğulu
Microtonal Guitar - Tolgahan Çoğulu
2 HN recommender · 2015–2022
2 mo on HNRichard Dawkins demonstrates the evolution of the eye
poejavlo
2 HN recommender · 2013–2023
4 mo on HNThe most feared song in jazz, explained
Vox
5 HN recommender · 2021–2025
1 mo on HNDid Time Start at the Big Bang?
PBS Space Time
1 HN recommend · 2020–2024
2 mo on HNSand Castle Holds Up A Car! - Mechanically Stabilized Earth
Practical Engineering
2 HN recommender · 2016–2026
18 mo on HNVectors | Chapter 1, Essence of linear algebra
3Blue1Brown
17 HN recommender · 2018–2026
15 mo on HNBut what is the Fourier Transform? A visual introduction.
3Blue1Brown
16 HN recommender · 2018–2025
14 mo on HNBut what is a neural network? | Deep learning chapter 1
3Blue1Brown
16 HN recommender · 2017–2025
13 mo on HNThe Beauty of Bézier Curves
Freya Holmér
16 HN recommender · 2021–2026
4 comments from Hacker News
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
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
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]
3Blue1Brown's video "Understanding e to the i pi in 3.14 minutes" is a nice compliment to this post. ▶ this video