Talk:William Shanks: Difference between revisions

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Is this the same Shanks, as in Shanks transformation of series? — Preceding unsigned comment added by 91.213.255.7 (talk) 04:22, 16 December 2011 (UTC)[reply]

In Shanks' publication there are two more errors:

 - from the 460th digit Shanks writes: '834' ( 6th column, before-last row ), this should be: '962'
 - from the 513th digit Shanks writes: '193' ( bottom of before-last column ), this should be: '065'

And then the already known error:

 - from the 528th digit Shanks writes: '50160...' ( bottom of first column ), this should be: '49463...'

itsme (talk) 00:29, 15 March 2022 (UTC)[reply]

As Matt Parker pointed out, W.Shanks corrected this later himself: https://royalsocietypublishing.org/doi/pdf/10.1098/rspl.1873.0010 itsme (talk) 13:11, 15 March 2022 (UTC)[reply]

I fully agree with that. How to insert this information properly into the article itself? Simply highlighting the errors in bold is not a solution in my opinion, so I reverted the last edit done by an anonymous user. --Uncopy (talk) 10:22, 20 June 2022 (UTC)[reply]

\center{Value of \pi}

In 1853 there appeared, in a paper by W. Rutherford, the value of the constant \pi to 530 decimals, calculated by W. Shanks. This was eventually extended by Shanks to 607, and in 1873 to 707 decimals.

For more than seventy years this has been accepted as the value of \pi, apparently without any doubts having been expressed in print.

Recently I decided to test numerically a series found by a colleague, R. W. Morris, namely

$$\pi = 12 \tan^{-1}{1\over 4} + 4\tan^{-1} {1\over 20} + 4\tan^{-1} {1\over 1985} $$

The value so obtained agrees with Shanks's value only to the 527th decimal place; from that last point it seems that Shanks's value is incorrect.

The values from the 521st to 540th decimals are given below:

86021 39501 60924 48077 (Shanks). 86021 39494 63952 24737 (D. F. F.).

It is of interest to note that the discrepancy occurs at about the point to which Shanks's first published value extends, that is, in the 530th decimal.

D. F. Ferguson Royal Naval College, Eaton, Chester. 2601:644:8501:AAF0:0:0:0:98EB (talk) 17:43, 21 May 2024 (UTC)[reply]