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Hello everyone!
This is the final installment of our investigation of the Gauss-Bonnet theorem! The proof given in this video and the inspiration of the series is from Richard Schwartz' book Mostly Surfaces (PDF here: www.math.brown.... I highly encourage you to check out the section on the Gauss-Bonnet theorem as well as the rest of the book because it is very interesting and well-written. If you want to learn more about the classic Gauss-Bonnet theorem, it is covered in any introductory differential geometry text book. (mathworld.wolf...)
I have one last video for this series which serves as behind-the-scenes/extra-information. Hopefully that should be out in the next few weeks!
See you soon!