Definitely not a brilliant approximation of pi, and it's not particularly beautiful either. I do find the one using Kepler's triangle beautiful, but opinions differ. It's often said that this is a coincidence, but I don't care, especially not in the case of the Great Pyramid. Perhaps the deviation for non-Euclidean space disappears entirely, who knows.

Below is the image of the original approximation as I found it. The use of Fraktur letters for the real and imaginary parts of the tetration of i is quite outdated and, moreover, not applied consistently. Here, I prefer the more modern and general notation Re(z) and Im(z).