William Feller's classic book on probability analyses the behaviour of waves --- your "regimes" --- in the sum of a sequence of coin tosses; I think the general heading is something like the "Petersburg paradox". Presumably the sequence of CF means behaves in a similar fashion. Is the corresponding higher-order behaviour known? And how well does your data fit the known modela? WFL On 12/29/12, Hans Havermann <gladhobo@teksavvy.com> wrote:
I have just determined that the geometric mean of 1498931686 terms (cherry-picked) of the *fractional* part of the continued fraction of pi is within 1.002405*10^-13 of Khinchin's constant.
And just to caution folk further about the nature of cherry-picking the number of terms: The geometric mean of 976 terms is closer to Khinchin's constant than the geometric mean of 2377934394 terms!
http://gladhoboexpress.blogspot.ca/2012/12/pi-continued-fraction-khinchin-re... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun