Science Frontiers ONLINE No. 53: Sep-Oct 1987 Issue Contents

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Pi And Ramanajan

Someone has finally complained about an equality sign in SF#37 namely,

22[PI]⁴ = 2143

D. Thomas has correctly pointed out that we have here only a very good approximation. Of course, one need not do the actual calculation to prove that it is an approximation, because 2143/22 is a rational fraction which can be expressed as a repeating decimal; whereas pi is irrational.

The number (2143/22)^¼ is a discovery of Ramanujan, about whom we heard on p. 000. How did he ever stumble upon this extremely accurate approximation of pi -- one that is accurate to 300 parts in a trillion? N.D. Mermin suggests that Ramanujan may have taken it from the expansion:

[PI]⁴ = 97 + 1/(2 + 1/(2 + 1/(3 + 1/(1 + 1/(16539 +....

If 16,539 is replaced by infinity, Ramanujan's result follows.

(Mermin, N. David; "Pi in the Sky," American Journal of Physics, 55:584, 1987.)

From Science Frontiers #53, SEP-OCT 1987. © 1987-2000 William R. Corliss

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Science Frontiers Sourcebook Project Reviewed in: Icarus: Volume 41, Issue 3, p. 470-470 1984, Vol.56:3, P.615 1983, Vol.58:3 June 1984, Vol.60:3 Dec 1984, Vol.72:3 Dec 1987 Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 1987 American Journal of Physics, Volume 52, Issue 8, p. 764 August 1984 Quotes "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