Regular Decagon Magic!

Can you find evidence of the golden ratio anywhere in this animation? If so, where? Explain. What is the measure of the pink angle? How do you know this to be true? See any Golden Triangles? See any Golden Gnomons? What is the exact value of the ratio of the brown segment to the segment with 3 hash marks? How can we formally prove any of the phenomena dynamically illustrated here?

Quick (Silent) Demo