In a message dated 10/02/00 07:19:48 GMT Standard Time,
[EMAIL PROTECTED] (Aaron Blosser) writes:
<<
What I'm getting at is that at some point, pi reaches a practical limit at
which expanding more decimal points is an abstraction because we could never
measure anything large enough for it to be useful. I mean, c'mon! The
universe is only so big! :-)
>>
This reminds me of a discussion I had years ago about the optimum design
for a currency. Most countries have coins/notes of value 1, 2, 5, 10, 20, 50,
100 basic currency units, but in Romaina I found they used 1, 3, 10, 30, 100
... multiples.
Presumably the object is to make it such that over an average of many
transactions, the minimum number of coins/notes changes hands. The
optimum ratio between successive currency units (notes/coins) seems to
be between 2 and 3, and a friend suggested that e (2.71828...) would be
the best value, i.e. we have coins and notes valued at 1, e, e^2, e^3 ...
cents or whatever. Maybe pi could be expressed exactly in such a
system. After all, e^(pi*i) = -1.
This led to a discussion as to whether or not it is possible to have a number
system based on a non-integer base. Maybe the great minds of GIMPS
can contribute to this.
Cheers, George.
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