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No. 9: Winter 1979

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Transcendental trivia?

Both e (2.7182...) and pi (3.1416...) are transcendental numbers of great significance in mathematics and the scientific description of nature. Instead of being neat and orderly (as we devoutly hope nature will be), the decimal expansions of these two numbers are patternless, some say ugly. Faint hope arises at the 710,150th digit of pi where a satisfying string of seven consecutive 3s appears (....353733333338...). More reassuring is the observation that (pi)4 + (pi)5 almost exactly equals e6 .

We are sure that great truths lie hidden in these two numbers (despite their unattractive decimals) when we find that a 5x5 magic square (first row: 17, 24, 1, 8, 15) can be transformed by the alchemy of pi into an unmagic but very strange square. To do this, replace the 17 by the 17th digit of pi (this is 2); 24 by the 24th digit (this is 4); and so on. The rows and columns of the new square add up to the same numbers: columns; 17, 19, 25, 24, 23; rows; 24, 23, 25, 29, 17. (Yes, the order given is correct.)

Gardner maintains that this astounding transformation is merely a coincidence, like all of the other peculiar relationships between 3 and pi. Millions and millions of relationships are possible and a few will certainly be remarkable, just as only a few of the many possible mathematical equations describe natural phenomena.

(Gardner, Martin, "Mathematical Games," Scientific American, 241:22, September 1979.)

From Science Frontiers #9, Winter 1979. 1979-2000 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