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For ? Day. 2015, Wolfram Research stirred up publicity with the blog “Pi or Pie?! Celebrating Pi Day of the Century (And How to Get Your Very Own Piece of Pi)”:
I grumbled that no self-respecting Deity would bother sending clues to worshipers dumb enough to use decimal instead of continued fractions (CF). However, in 2019 we’re barely able to afford a full CF version of Wolfram’s birthday games. Assuming GaussKuzmin distribution, define
Then
I.e, 41.5% of terms should be 1, 17% should be 2, etc.
But cfprob also gives us the probabilities of term sequences:
(Invariant under reversal but not shuffling.)
This says to expect about six 1,2,3’s in every burst of 1000 terms:
Try a million :
(0.5 seconds for a million terms. Have I actually lived to see this?)
Continued fractions accommodate fancier date formats:
Sure enough, there were two of them.
But for really fancy dates,
we’ll need Eric Weisstein’s record ? CF calculation.
Utility functions
These are the definitions of the utility function tim you will need for the above evaluations:
Birthday-Dates-Using-Pi-Continued-Fractions-by-Bill-Gosper.nb (29.8 KB)