Re: Repeated digits in Pi -- the Feynman point

richard@cogsci.ed.ac.uk (Richard Tobin) writes:

In article <103k5nq$3ju79$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:
>

3.14159 26535 89793 23846 26433 83279       41971 69399 3751...

 3.14159 26535 89793 23846 26433 83279 50288 41971 6939...

>
(reformatted)
>
Presumably the first was copied from a listing in groups of 5 digits,
and one group was missed out.
>

Oh, who decides?

>
A substantial proportion of the population are capable of learning the
necessary maths and writing a program to determine which is correct.
A much smaller proportion are sufficiently motivated to do so.
>
If you don't trust the computer, it would be possible to use the
formula
>
  pi = 16 atan(1/5) = 4 atan(1/239)
>
to calculate it by hand to that precision.  William Shanks used it and
obtained 527 decimal places correctly in 1853.  This was not surpassed
(and an error found in his later digits) until 1946 using a mechanical
calculator.

By hand, I think I'd favour the spigot method. I know Matt Parker
(/Stand-Up Maths/ on youtube) likes to organise the manual calculation
of pi on "pi day", and I'm a little disappointed he's never tried
spigot. I think its Big-Oh is superior to any of the algorithms that
effectively do arbitrary precision arithmetic, as you never need to deal
with numbers much bigger than a hundred.

Phil
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