🚀 go-pugleaf

In article <zZIi7jAzW8c3EwDD@merlyn.demon.co.uk>,
  Dr John Stockton <jrs@merlyn.demon.co.uk> wrote:
> JRS:  In article <Im0c0MABmjc3Ew2K@merlyn.demon.co.uk> of Thu, 24 Jun
> 1999 14:58:25 in news:comp.lang.pascal.delphi.misc, Dr John Stockton
> <jrs@merlyn.demon.co.uk> wrote:
> >
> >It will be interesting to see whether you've managed to avoid using a
> >value for Pi, implicitly or explicitly, in the work.
>
[...]
> I wonder whether there is a method of doing Buffon which does not use
Pi
> (implicitly or explicitly), does not have a subset-capability of
> determining Pi, and does not, as Buffon did, use the Real World?

       I have no idea what a "subset-capability" is, but modulo
that of course there is. Set one endpoint P1 of the needle to a
random point in a large square. Then set the other endpoint
to another random point. Reject the second endpoint until you
get one with say 0.5 < |P1 - P2| < 2. Then rescale it so
|P1 - P2| = 1. There's your random needle, no trig and hence
no Pi required.

   ("rescale": say P2 := P1 + (P2 - P1)/|P2 - P1| . No
angles, just a square root.)

> ISTR that it is established that more rapid convergence is obtained if
> you glue the needles together in pairs, at right angles - centrally is
> usual but I think not necessary; more rapid even if one counts needles
> rather than throws.
>
> It must be better still to glue large numbers, evenly distributed in
> angle, together - centrally to get a disc, or endwise to get a ring.
> Not too many, though; with an infinite number of needles, unless
> carefully treated, there's a risk of getting infinity/infinity as the
> result.

     Huh? The limit in question _is_ a limit "of the form
infinity/infinity". I don't think there's much danger of
the actual algorithm running infinitely many times.

> I guess that the true intention was to draw attention to the services
> you provide at efg's Computer Lab (http://www.efg2.com/lab) - ISTM
that
> it is working.
>
> --
>  � John Stockton, Surrey, UK.  jrs@merlyn.demon.co.uk   Turnpike v4.00
  MIME. �
>   Web <URL: http://www.merlyn.demon.co.uk/> - TP/BP/&c. FAQqish topics
& links.
>   Timo's TurboPascal <A
HREF="ftp://garbo.uwasa.fi/pc/link/tsfaqp.zip">FAQ</A>.
>   <A HREF="http://www.merlyn.demon.co.uk/clpb-faq.txt">Mini-FAQ</A> of
c.l.p.b.
>


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