Tuesday, 16 April 2013

William Shanks and Pi (NZ345499)

Pi, the ratio of a circle’s circumference to its diameter, is perhaps the most famous of our mathematical constants. It has fascinated many of the brightest sparks in the history of mankind, often dominating the thoughts of far too many for far too long. It even has a film of its own.

Just as strangely fascinating as pi itself are the odd-ball folk who have, over the years, dedicated large chunks their lives to its calculation. Yes, mathematicians are strange creatures, and the extraordinary William Shanks was no exception.

In the long chronology of the computation of pi, that of Mr Shanks’ is right up there with the best of them. And he was a North-East boy: born in Corsenside, Northumberland, but who lived out the final several decades of his life in Houghton-le-Spring. He settled there in 1847 after marrying his wife, Jane, in London the previous year.

He owned and ran (and lived in) a private boarding school in Nesham Place, an activity which afforded him plenty of time to indulge his passion for sums and such like. He was soon publishing works on mathematics, and began working on the expansion of pi at an early stage. Beginning in the early 1850s, he pushed the computation of the famous constant out beyond 500 decimal places – then 600, then finally (in 1873, after a bit of a rest) claimed a whopping 707. During his ‘gap years’ of 1850s-early 1870s he worked on many other mathematical problems, including the calculation of e and Euler’s Constant y to more decimal places than ever before. He also published a table of prime numbers up to 60,000, found the natural logarithms of 2, 3, 5 and 10 to 137 places, and a whole host of other bits and bobs.

Shanks’ work on pi remained unchallenged (and unbettered) until 1946, when his landmark 707 decimal places was found to contain an error at the 528th place when a certain D.F.Ferguson tapped the problem into his desk calculator. Shanks’, on the other hand, had no such luxury of course. He would work for hours, manually, on his little problems most mornings, then check for errors in the afternoons – taking him a good twenty years get as far as we can get in a split second today.

William Shanks died, aged 70, in 1882, and was buried in nearby Houghton Hillside Cemetery

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