Re: [math-fun] 5000 billion digits of Pi
I think I'm missing something. --Dan << In the invariant measure* on (0,1], the number N has probability P(N) = log_2( 1 + 1/(N(N+2)) ) * I.e., with density d(x) = (1/log(2)) 1/(x+1), invariant under the map T(x) = 1/x - [1/x]. _____________________________________________________________________ << Correction: P(n) = (1/log 2) log((n+1)^2/n(n+2)).
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
Sorry Dan, It was my error. I misread log_2 as log(2) rather than the function log to base 2. -- Gene ________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Fri, August 6, 2010 7:15:59 PM Subject: Re: [math-fun] 5000 billion digits of Pi I think I'm missing something. --Dan << In the invariant measure* on (0,1], the number N has probability P(N) = log_2( 1 + 1/(N(N+2)) ) * I.e., with density d(x) = (1/log(2)) 1/(x+1), invariant under the map T(x) = 1/x - [1/x]. _____________________________________________________________________ << Correction: P(n) = (1/log 2) log((n+1)^2/n(n+2)).
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Eugene Salamin