What is Euler's formula actually saying? | Lockdown math ep. 4
3Blue1Brown 3Blue1Brown
0 subscribers
16K 151

 Published On Apr 28, 2020

What does it mean to compute e^{pi i}?
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks

Beautiful pictorial summary by @ThuyNganVu:

Video Timeline (Thanks to user "Just TIEriffic")
0:00:00 Welcome
0:00:20 Ending Animation Preview
0:01:15 Reminders from previous lecture
0:03:30 Q1: Prompt (Relationship with e^iθ=…)
0:05:40 Q1: Results
0:07:15 WTF, Whats The Function
0:10:00 Exploring exp(x)
0:11:45 Exploring exp(x) in Python
0:14:45 Important exp(x) property
0:15:55 Q2: Prompt (Given f(a+b) = f(a)f(b)…)
0:17:30 Ask: Which is more interesting, special cases or the general case
0:20:00 Q2: Results
0:23:50 Will a zero break Q2?
0:25:40 The e^x convention
0:27:10 Q3: Prompt (i^2 = -1, i^n = -1)
0:27:45 Ask: Zero does not break Q2
0:30:20 Q3: Results
0:31:05 Comparison to Rotation
0:33:00 Visualizing this relationship
0:36:50 The special case of π
0:39:20 Periodic nature of this relationship
0:39:40 Q4: Prompt (e^3i)
0:41:35 Q4: Results
0:43:55 Explaining the celebrity equation
0:45:55 Homework / Things to think about
0:49:15 Ask: Zero does break Q2.
0:50:30 Closing Remarks
The live question setup with stats on-screen is powered by Itempool.

Curious about other animations?

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.


3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown

show more