Happy belated pi day

Friday 16 March 2012

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!

tagged: » 2 reactions

Comments

[gravatar]
Joe 7:57 AM on 17 Mar 2012

If I'm not mistaken, most of the world outside the United States writes the date as 14.3 or 14/3, and a few as 2012.3.14. So I'd say it's only Americans who can consider it Pi Day. Also, if Augustus hadn't taken a day away from February, Pi Day would be a day earlier. And of course, why should the year start on 1st January instead of what is now 21 March, or other days (as observed by other religions). Pi Day would make more sense in terms of the orbit of the Earth, i.e., something like one radian of the orbit.

[gravatar]
Nick 12:12 AM on 19 Mar 2012

I used to celebrate pi day before I converted. Now I am a Tauist. http://tauday.com/

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