Pi and the Mandelbrot Set - Numberphile

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. [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. [VIDEO]

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: [VIDEO]