Pi day (two days ago) passed without notice here, but then Eric Johnson posted a comment on last year’s pi day post:
Ancient Egyptians may have thought Pi was 256/81: Approximations of π.
256/81 is about 3.16049382716049382716, which is approx 0.6% above the value of Pi. 22/7 is approx 0.04% less than Pi, so the ancient Egyptians weren’t particularly accurate, but the numerator and denominator they choose are interesting for another reason.
256/81 can be expressed as 2^8 / 3^4, which can be expressed as 2^2^3/3^2^2, which of course is a palindrome.
Posted on A.E. Pi day, 2012 (A.E. = Ancient Egyptian)
I had never heard any of this before, and was delighted.
Poking around on the Wikipedia page about approximating pi, I found this interesting tidbit: there are points in the Mandelbrot set whose iteration escape counts provide arbitrarily accurate estimates to pi! Will the wonders never cease?
Happy belated Pi Day!