My absolute favorite numberphile video is how pi occurs in a peculiar way with Riemann Zeta/Mandelbrot. Maybe it only amazes me because I don’t have a PhD in math, but it just seemed so strange how pi shows up in this video. [this video]
I really enjoyed this video with Dr Holly Krieger of Numberphile. [link] There are a few more videos related to PI and The Mandelbrot set, Julia, etc. All nice to watch. [this video]
Numberphile with Holly Krieger on pi and Mandelbrot
When you begin with z = k i - 0.75, you can obtain an arbitrarily good approximation of pi by multiplying the p for which f_p(z) = z^2 + z diverges by k . The approximation increases in precision as k tends to 0. There's a neat video explaining it here: [this video]
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