🚀 go-pugleaf

JRS:  In article <7l357k$4m6$1@nnrp1.deja.com> of Sat, 26 Jun 1999
18:13:14 in news:comp.lang.pascal.delphi.misc, David C. Ullrich
<ullrich@math.okstate.edu> wrote:
>In article <zZIi7jAzW8c3EwDD@merlyn.demon.co.uk>,
>  Dr John Stockton <jrs@merlyn.demon.co.uk> wrote:

>       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.)

ISTM, seemingly confirmed by test, that your method does not give a
uniform distribution of angles.


>> 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.

With an infinite number of needles glued together, the algorithm need
only be run once - though this will take infinite time.
 
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