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No. 96: Nov-Dec 1994

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Lazzarini eats humble pi (posthumously)

If you are on a desert island and have forgotten the value of pi and need it desperately, you can find it experimentally. One amusing though tedious method would require throwing a short, straight twig onto parallel lines drawn in the beach sand. You will be able to compute pi from:

pi = 2lN/dH,

where l = the length of the twig, which must be less than d, separation of the parallel lines. N = the number of throws. H = the number of times the twig crosses one of the lines.

One famous performance of this experiment was by M. Lazzarini in 1901. He reported that in 3408 throws he got 1808 intersections, leading to:

pi = 3.1415929

Actually, the final digit should be a 6. Thus, Lazzarini measured pi to a few parts in 10 million.

Recently, L. Badger, Weber State University, concluded that Lazzarini probably never actually performed his experiment. His results were just too good -- too fortuitous! If the number of hits had been 1807 or 1809, pi would have been wrong by 1 part in 2,000.

As it turns out, a Chinese mathematician of the 5th Century pointed out that 355/113 = 3.1415929. It is very suspicious that Lazzarini's 3408 = 355 x 16, and 1808 = 113 x 16. Badger thinks that Lazzarini's experiment was only a "thought" experiment based on the ratio 355/113.

(Maddox, John; "False Calculation of Pi by Experiment," Nature, 370:323, 1994.)

From Science Frontiers #96, NOV-DEC 1994. 1994-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:

Quotes

  • "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