use each digit (from the given base set) just once to produce the best possible approximation of Pi
Alexander Povolotsky
apovolot at gmail.com
Tue Mar 25 14:06:59 CET 2008
Greetings to All,
I noticed that
689725314 / 219546387 = 76636146 / 24394043 = 3.141592642...
Of course the *quality of approximation" is very poor (16 digits "in"
are yielding just 8 accurate digits) but please note that in the ratio
below
6897253140 / 2195463870
all 10 digits of the decimal base (from 0 to 9) are used just once in
both numerator and denominator.
I hope that I found the *best* combination of digits for both
numerator and denominator (but I am notsure since I've done it late
night by hand).
I wonder if anyone would be interested to see what other (than decimal
) base systems could give with regards to the same approach of using
each digit (from the given base set) just once to produce the best
possible approximation of Pi.
If results are interesting, then one could compose two sequences (for
numerators and denominators) where a(10) will be correspondingly
6897253140 and 2195463870.
Regards
Alexander R. Povolotsky
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