Vectors are more awesome than you think (#SoME2)

There we have it, my entry for the second Summer of Math Exposition, hosted by 3blue1brown. In this video I explain why vectors are so much more useful than they might seem at first glance, and I do this by building up to an unexpectedly simple proof of the addition formulas for sine and cosine. These are normally proved using a rather roundabout way, but using vectors we can gain a deep insight into what they are really all about. I’m super pleased with how this one turned out in the end. The idea behind it has been on my mind for about two years now, and I really feel like I couldn’t possibly have done better to reach my vision of what this video would end up being, especially given that this is my first major project in Manim. So yeah, no matter how it ends up doing in the overall competition surrounding SoME2, I’m super proud of what I’ve managed to create here. Music by Vincent Rubinetti Download the music on Bandcamp: Stream the music on Spotify: Royalty free images used are from unsplash and wikimedia commons. Relevant timestamps: Before the awful proof 00:00-02:30 Torture session 02:30-05:51 Motivation 05:51-08:46 Intro to vectors 08:46-10:38 2-dimensional vectors 10:38-17:04 Creating a dictionary 17:04-25:12 Rotations 25:12-29:49 A beautiful proof 29:49-33:06