How do you study what cannot be solved?

Home page: https://3blue1brown.com/

Brought to you by you: http://3b1b.co/de1thanks

Need to brush up on calculus? https://youtu.be/WUvTyaaNkzM

Error correction: At 6:27, the upper equation should have g/L instead of L/g.

Steven Strogatz NYT article on the math of love:

https://opinionator.blogs.nytimes.com/2009/05/26/guest-column-loves-me-loves-me-not-do-the-math/

Interactive visualization of the example from this video, by Ilya Perederiy:

https://www.expunctis.com/2019/04/04/vtvt-another-demo.html

If you’re looking for books on this topic, I’d recommend the one by Vladimir Arnold, “Ordinary Differential Equations”

Also, more Strogatz fun, you may enjoy his text “Nonlinear Dynamics And Chaos”

Curious about why it’s called a “phase space”? You might enjoy this article:

https://www.physics.umd.edu/courses/Phys404/Anlage_Spring10/The%20TangledTaleofPhaseSpace.pdf

From a response on /r/3blue1brown, here are some interactives based on examples shown in the video:

https://observablehq.com/@tophtucker/tales-from-the-romeo-and-juliet-phase-space

https://observablehq.com/@mbostock/predator-and-prey

Animations 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 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:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

## 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:

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Twitter: https://twitter.com/3blue1brown

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Instagram: https://www.instagram.com/3blue1brown_animations/

Patreon: https://patreon.com/3blue1brown

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