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Shanks, Ferguson and π

Published online by Cambridge University Press:  03 November 2016

Extract

Fifty or sixty years ago, any forward schoolboy (to borrow a phrase from Macaulay) knew that a man called Shanks had calculated the value of π to 707 places of decimals. Who Shanks was, why he should have performed this Gargantuan feat, and why he should have stopped, if not from exhaustion, at the 707th place, were questions that may have been asked but were seldom answered. The bald statement is still to be found in a number of recent books, but it is not often brought up to date by noting the interesting sequel, that round about 1944 a member of this Association, D. F. Ferguson, re-calculated πby a formula similar to but different from that used by Shanks, and discovered that Shanks had made a mistake and that his value was incorrect after the 527th place.

Type
6. Return to 1971
Copyright
Copyright © Mathematical Association 1971

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References

* It is in fact given in Loney’s Plane Trigonometry.

In the M.T.A.C. note, the digits in places 731-740 should read 59813 62977, and those in places 796-800 should read 31859.