Yesterday being pi-day (3/14 at approximately 1:59:27), I tried a little
exercise. The most commonly used approximations for this nasty little
number are 3.1416, 22/7, and 355/113. Since pi is 3.14159... 3.1416 is a
pretty good approximation, and only requires you to remember five
digits. 22/7 only needs 3 digits, while 355/113 needs a prodigious act
of memory on SIX whole digits [shocked muttering from audience].
Their relative merits, taking 3.14l6 as the baseline, has 22/7 with 172x
the error of our baseline. Amazingly, hexadigital 355/113 has only 3.6%
of the error of the best 5 digit champion, 3.1416! In between, there is
very little to challenge this. 311/99 only requires you to memorize five
digits, but has 24x the baseline error, so it's by far second best to
just remembering the number itself.
All in all, 355/113 seems a miracle of parsimony. For the cost of
memorizing one more digit, you get a gigantic jump in accuracy.
Happy Pi Day*
Jack Tingle
That's US civil Pi Day. European civil and US military Pi Day is 31
April. ;)
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