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No. 103: Jan-Feb 1996

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How To Find A Piece Of Pi

The formula shown below allows one -- if one wishes -- to find the billionth digit of pi without first computing the preceding 999,999,999 digits. In other words, isolated digits of pi can be quickly calculated should an urgent need arise. P.B. Borwein et al, at Simon Fraser University, announced this "curious" discovery in October 1995.

Equation mathematicians use in calculating isolated digits of pi
This is the equation mathematicians use in calculating isolated digits of pi.
Innuendo aside, there is something more than "curious" here. It seems that the formula works only for hexadecimal (base-16) digits of pi. These can be easily converted into binary (base-2) digits. Strangely, it does not work at all for our familiar decimal (base-10) digits of pi.

Not to worry though! Y. Kanada and colleagues, at the University of Tokyo, have now computed pi to 4,294,960,000 decimal digits. But, they have found a puzzling asymmetry. In the first 4 billion digits, the decimal digit 6 occurs 400,033,035 times, but 2 shows up only 399,965,405 times! Shouldn't all ten digits appear with the same frequency? Obviously, we do not appreciate all of the subtleties of pi.

(Peterson, I.; "A New Formula for Picking Off Pieces of Pi," Science News, 148:279, 1995.)

From Science Frontiers #103, JAN-FEB 1996. 1996-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:


  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987