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Old 2003-01-27, 21:59   #34
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I was going to say something about pi and rationality, but someone beat me to it ops:
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Old 2013-09-09, 23:54   #35
Kathegetes
 
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Quote:
Originally Posted by cheesehead View Post
Pi is irrational and transcendental in all integer number bases. Generally, ease of computing its value in a particular base depends only on the computer's ease of calculation in that base, not on how Pi's value is expressed in that base. This applies both to floating-point arithmetic and fixed-point arithmetic.

Most recent Pi calculations by digital computer have been performed in base 2 or base 16, not base 10, because those computers operate more efficiently in base 2 or 16 than in base 10.

A famous Bailey-Borwein-Plouffe algorithm for Pi features the number 16 prominently, making its use in base 16 particularly efficient. But similar algorithms can be derived that feature integers other than 16 and would be efficiently computed in number bases other than base 16.
I always wanted to know about that.
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