The essence of calculus

What might it feel like to invent calculus? Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to share the videos. Special thanks to these supporters: http://3b1b.co/lessons/essence-of-calculus#thanks In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus. Thanks to these viewers for their contributions to translations Dutch: @LFWarsen, Lauri Warsen Hebrew: Imri, Omer Tuchfeld Hindi: Vinayak Hungarian: homok43 Italian: @Deye27, @hi-anji, alberto alessi Korean: Hana Seo Portuguese: redkk123 Spanish: @agustin-j Vietnamese: @ngvutuan2811, ngvutuan ------------------ 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: 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown