Understanding e to the i pi in 3.14 minutes | DE5

Watch on YouTube

Show annotations

Download is disabled.




Genre: Education

Family friendly? Yes

Wilson score: 0.9924

Rating: 4.974 / 5

Engagement: 4.14%


Subscribe | 2.3M

Shared July 7, 2019

Euler's formula intuition from relating velocities to positions.
Home page: https://www.3blue1brown.com
Yeah yeah, the runtime is 4:08, but it's 3.14 minutes to the conclusion.

Not familiar with the calculus referenced in this video? Try taking a look at this one:

Another perspective on this formula, from Mathologer:

Another perspective from this channel:

And yet another from the blog Better Explained:

I'm not sure where the perspective shown in this video originates. I do know you can find it in Tristan Needham's excellent book "Visual Complex Analysis", but if anyone has a sense of the first occurrence of this intuition do feel free to share. It's simple and natural enough, though, that it's probably a view which has been independently thought up many times over.


These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

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...
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown