🚀 go-pugleaf

Checksum: 2743647618 (verify with brik -cv)
Submitted-by: DANIEL COHEN-LAROQUE <COHEN_LA@eldi.epfl.ch>
Posting-number: Volume 7, Issue 18
Archive-name: approxpi.dcl

BEGIN_DOC approxpi.doc

   Hi all,

There are so many algorithms for finding the number PI that it
was difficult not to try a few ones.
The following program uses the MonteCarlo's method which is based
on the repartition of random numbers:
         
   |-----------|
   | -       - |
   |-         -|
   |-         -|
   | -       - |
   |-----------|
          
If the radius of the circle is r then the surface inside is PI*r^2=S1
The surface inside the entire square is immediately S2=4*r^2

So, the ratio S1/S2 gives PI/4 and stands for the ratio between
the points droped inside the circle and the ones inside the square!
Don't expect this method to be accurate: the best result I obtained
is about 2% (relative error) with 5'000 points...

This simulation has no scientific purposes and is completely useless. 
However, I post it because of the originality of the method. 
A French expression says:"Le hasard fait bien les choses!" 

Mail me the American translation or any comments to:
Daniel COHEN-LAROQUE
Swiss Federal Institute of Technology
cohen_la@eldi.epfl.ch

END_DOC

BEGIN_RPL approxpi.rpl
%%HP: T(3)A(R)F(.);
@ Approxime par la methode de MonteCarlo
DIR
  GO
    \<< 0 0 \-> n in
      \<< INIT
        DO RANDXY
"PLOTING POINTS"
WARN 1 10
          START \GS-
V\-> \->V2 DUP (-3.3,0)
- ABS 3.1 \<=
            \<< 'in'
INCR DROP
            \>> IFT
PIXON 1000 .02 BEEP
          NEXT
"UPDATING RESULT"
WARN 'n' 10 STO+
PICT (4.1,1.5) n
\->STR 1 \->GROB REPL
in n / 4 * \-> t
          \<< PICT
(1.6,-.5) t 10 RND
1 \->GROB REPL PICT
(3.3,-1.5) t \pi \->NUM
%CH ABS 2 RND 1
\->GROB REPL
          \>>
        UNTIL KEY
        END DROP
"ON TO EXIT" WARN {
} PVIEW
      \>>
    \>>
  WARN
    \<< 1 \->GROB \-> s
      \<< PICT
(.4,-2.4) PICT
(.1,-2.2) # 63d
# 9d BLANK NEG REPL
s GXOR
      \>>
    \>>
  RANDXY
    \<< 0 RDZ
"WAIT RANDOM #"
WARN 1 10
      START RAND
6.2 * 6.4 - RAND
6.2 * 3.1 - 2 \->ARRY
1 RND \GS+ 800 .01
BEEP
      NEXT
    \>>
  INIT
    \<< -19 SF STD
RAD PICT PURGE {
# 0d # 0d } PVIEW {
# 32d # 32d } # 31d
0 6.3 ARC { # 1d
# 1d } { # 63d
# 63d } BOX PICT {
# 69d # 3d }
"Computing:" 2
\->GROB REPL { # 129d
# 63d } { # 66d
# 1d } BOX { # 129d
# 12d } { # 66d
# 12d } LINE PICT
(.3,1.5)
"# POINTS: 0" 1
\->GROB REPL PICT
(.4,.5) "\pi: " \pi
\->NUM 10 RND + 1
\->GROB REPL PICT
(.4,-.5) "PI: 0" 1
\->GROB REPL PICT
(.4,-1.5)
"\GDr [%]: \oo" 1 \->GROB
REPL
    \>>
  PPAR {
(-6.5,-3.1)
(6.5,3.2) X 0 (0,0)
FUNCTION Y }
END
END_RPL


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END_UU