In this video, I derive my visual proof for the Law of Cosines. Similar to the popular Pythagorean Theorem proof, this proof also compares the areas of two figures. The goal of this video is to provide an intuitive explanation for the existence of the trigonometric term in the Law of Cosines. I assume, if you're watching this, that you are far enough in your math education to know what the Law of Cosines is and how to use it. That is, you should know high school Geometry and some basic Trigonometry.

I came up with this generalization myself a few months ago. As I was making this video, I saw another "area comparison" proof on Wikipedia. However, I think the one in this video is different enough in its construction (and, frankly, more beautiful) that I can still claim that it is original. Please let me know if it isn't!

I want to thank Grant of 3B1B and everyone involved in the development and documentation of Manim CE, which I used to make this video, as well as everyone organizing the Summer of Math Exposition. I also want to shout out Micro Math Visual Proofs, whose videos inspired me to go looking for more visual proofs.

This is my first time making anything with Manim, and it probably shows. Regardless, I hope you all enjoy watching!