🚀 go-pugleaf

In article <3775731b.19624768@netnews.worldnet.att.net>,
  drifkind@acm.deleteme.org (David Rifkind) wrote:
> On Sat, 26 Jun 1999 20:01:09 GMT, drifkind@acm.deleteme.org (David
> Rifkind) wrote:
> >On Sat, 26 Jun 1999 18:13:14 GMT, David C. Ullrich
> ><ullrich@math.okstate.edu> wrote:
> >>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.)
> >
> >Will that give an even distribution of angles?  It seems like it
ought
> >to give some sort of bias towards rectangular angles.  (Old joke
time:
> >Is there a STATISTICIAN in the house?)
>
> Ohhh...never mind.

     Too late. If anyone else is wondering what the problem was,
or is maybe wondering about the same (non-)problem: note the
words "Reject the second endpoint until you get one with say
0.5 < |P1 - P2| < 2."

     (Of course a person wouldn't actually choose a brand-new
P2, a person would choose P2 at random in a small square
centered at P1, trying til he got one in that annullus.)

> "Generally speaking, things have gone about as far as they can
possibly
> go when things have got about as bad as they reasonably get."
>


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