posted on Jan, 5 2013 @ 12:34 AM
From wikipedia, "pi":
The digits of π have no apparent pattern and pass tests for statistical randomness including tests for normality; a number of infinite length
is called normal when all possible sequences of digits (of any given length) appear equally often. The hypothesis that π is normal has not
been proven or disproven. Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis.
Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the
frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found. Despite the fact that
π's digits pass statistical tests for randomness, π contains some sequences of digits that may appear non-random to non-mathematicians, such as the
Feynman point, which is a sequence of six consecutive 9s that begins at the 762nd decimal place of the decimal representation of π.
"Normality" is the property the teacher is speaking of. While pi seems to be normal in this sense, there is no proof that there is; proof would seem
to involve having all the digits of pi available for inspection, and that is plainly impossible.
My favorite story about pi is contained in Sagan's
Contact (the book, not the movie). The following constitutes a spoiler, so read no further
if you want to try the book out itself. (Pardon, I don't have a copy here, so my telling may be off in details.)
In the story the protagonist is given a hint by an ET (her father, at least in form) that there is a message from the Creator hidden in the expansion
of pi. She sets up a program like SETI@Home to work on it. At the end of the book, the computer tells her that when pi is expanded in base 11, some
100,000 digits in, the expansion suddenly breaks into 599 zeros, a 1, and then 597 zeros and three 1s, and proceeds in that fashion of 1s and 0s for
160,000 digits, and then returns to random digits. When plotted on a 400x400 raster, the 1s form a circle on a 0 background. (The idea of using
numbers in a rectangular raster to present pictures is used so often earlier in the book that by now, what's happening is obvious even to non-maths.)
This is, of course, the source of much wonderment in the last two paragraphs in the book, about a universal Creator who has the power to bend a
universal constant to his will.
But (and this isn't from the book) if normalcy for pi is true, then this fictional pattern may mean nothing at all, just the fulfillment of a promise
from normalcy. Of course, Sagan was an astronomer, not a mathematician.
edit on 5-1-2013 by puncheex because: add a little
explanation