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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 563 "PROGRAM:  BuffonsNeedle
\nCALLING SEQUENCE:  BuffonsNeedle(n, show)\nPARAMETERS:\n     n - an \+
integer\n     show - a Boolean variable (true or false)\nSYNOPSIS:\n  \+
   -  This program simulates the Buffon needle experiment described in
 the book,\n        dropping n pins on an 8 x 8 grid.  The program pri
nts an estimate for Pi, using\n        the book's method.  If show = t
rue, a graphical display of the experiment is\n        produced, showi
ng every tenth pin. \nRETURNED VALUES:\n     -  none\nLOCATION:\n     \+
Folder:  Chapter 2\n     File:      \"BuffonsNeedle.Chpt2.map.r4\"" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 866 "\n\nBuffonsNeedle:=proc(n,show)\n
\011local a,b,i,ends,U,angles,twopi,j,needles,x1,y1,x2,y2,theta,pictur
es,R,\n\011\011\011test1,test2,counter,x:\n\011with(stats):\n\011R:=ra
ndom[uniform[0,8]]('generator'):\n\011ends:=[seq(evalf(R()),i=1..(2*n)
)]:\n\011twopi:=evalf(2*Pi):\n\011U:=random[uniform[0,twopi]]('generat
or'):\n\011angles:=[seq(U(),i=1..n)]:\n\011needles:=NULL:\n\011counter
:=0:\n\011for j from 1 to n do\n\011    x1:=op(2*j-1,ends):\n\011\011y
1:=op(2*j,ends):\n\011\011theta:=op(j,angles):\n\011\011x2:=x1+cos(the
ta):\n\011\011y2:=y1+sin(theta):\n\011\011test1:=min(y1,y2):\n\011\011
test2:=trunc(max(y1,y2)):\n\011\011if test1<=test2 then counter:=count
er+1 fi:\n\011\011if show=`true` then\n\011\011\011if (j mod 10)=0 the
n\n\011\011\011\011needles:=needles,line([x1,y1],[x2,y2]):\n\011\011
\011\011gc():\n\011\011\011fi:\n\011\011fi:\n\011od:\n\011print(evalf(
(2*n)/counter));\n\011if show=`true` then\n\011\011i:='i':\n\011\011x:
='x':\n\011\011with(plots):\n\011\011a:=plot([8,x,x=0..8]):\n\011\011b
:=seq(plot(\{i\},x=0..8),i=1..8):\n\011\011display([a,b,needles]);\n
\011fi:\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "BuffonsNee
dle(1000,true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+]A2%G$!\"*" }}
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