{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "
Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 
0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Fixed Width" 0 17 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }3 0 0 -1 
-1 -1 0 0 0 0 0 0 17 0 }{PSTYLE "" 17 256 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 111 "Example: Use Maple to estimate the probability of throwing two
 points in a 1x1 squre having distance less than " }{XPPEDIT 18 0 "s;
" "6#%\"sG" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 82 "The experiment: throwing two points. results: t
wo \"locations\" (x1, y1), (x2, y2). " }}{PARA 0 "" 0 "" {TEXT -1 58 "
To simulate: we need to get random number x1, x2, y1, y2. " }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Input: s, n" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 745 "\ntwop
oint:=proc(\n                s::numeric,\n                n::integer\n
               )\n   local dis, x1, x2, y1, y2, count, i;\n\n   if n <
= 0 then\n      print(`n should be a big, positive integer`);\n      R
ETURN():\n   fi;\n\n   count:=0;\n   for i from 1 to n do\n\n      # s
imulation\n      x1:=real_ran(0,1);\n      y1:=real_ran(0,1);\n      x
2:=real_ran(0,1);\n      y2:=real_ran(0,1);\n\n      # checking\n     \+
 dis:=sqrt( (x2-x1)^2 + (y2-y1)^2 );\n      if dis < s then\n         \+
count:=count+1;\n      fi;\n\n   od;\n\n   evalf( count/n );\n\nend;\n
\n#\n# function that output a random real number in [a,b]\n#\nreal_ran
:=proc(\n               a::numeric,\n               b::numeric\n      \+
        )\n   local x;\n   x:=rand();\n   evalf( a+ (b-a)*x/9999999999
99 );\nend;\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 23 "read(`a:twopoint.txt`);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%)twopointGR6$'%\"sG%(numericG'%\"nG%(integerG6)%$disG
%#x1G%#x2G%#y1G%#y2G%&countG%\"iG6\"F5C&@$19%\"\"!C$-%&printG6#%Dn~sho
uld~be~a~big,~positive~integerG-%'RETURNGF5>8)F:?(8*\"\"\"FFF9%%trueGC
(>8%-%)real_ranG6$F:FF>8'FK>8&FK>8(FK>8$-%%sqrtG6#,&*$),&FQFFFJ!\"\"\"
\"#\"\"\"FF*$),&FSFFFOFgnFhnFinFF@$2FU9$>FC,&FCFFFFFF-%&evalfG6#*&FCFi
nF9!\"\"F5F5F5" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)real_ranGR6$'%\"a
G%(numericG'%\"bGF)6#%\"xG6\"F.C$>8$-%%randGF.-%&evalfG6#,&9$\"\"\"*&,
&9%F9F8!\"\"F9F1F9#F9\"-************F.F.F." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "twopoint(1.0, 1000);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+++++(*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "twop
oint(0.5, 10000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++>[!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "twopoint(2,0);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%Dn~should~be~a~big,~positive~integerG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 8 0" 89 }
{VIEWOPTS 1 1 0 1 1 1803 }