;** Pi nach Euler
;** 22.10.2005 by Triton
;** pi²/6=1/1² + 1/2² + 1/3² + 1/4² + ...
Graphics 640,480,16,2
AppTitle "Pi nach Euler"
SetBuffer BackBuffer()

While Not KeyDown(1)
   Text 10,10, "n = "+ n
   Text 10,30, "Pi = "+ eulerpi#(n)
   n=n+1
   Flip
   Cls
Wend
End

;---
Function EulerPi#(n)

For a=1 To n
   b=a*a
   c#=c+1.0/b
Next
Return Sqr(6*c)

End Function

;** Pi nach Triton ;D
;** 22.10.2005 by Triton
Graphics 640,480,16,2
AppTitle "Pi nach erweiterer Monte Carlo-Methode"

While Not KeyDown(1)
   Text 10,10, "n = "+ n
   Text 10,30, "Pi ~ "+ tritonpi#(n)
   Text 10,50, "Pi = "+Pi
   n=n+1
   Flip
   Cls
Wend
End

;---
Function TritonPi#(r)

For x=0 To 2*r
   For y = 0 To 2*r
      abst#=Sqr((x-r)*(x-r)+(y-r)*(y-r))
      If abst# <= r Then a = a + 1
   Next
Next
Return a/r^2

End Function


;---
;Prinzipiell schnellere Fkt, die aber
;durch BB-Rundungsfehler ungenauer ist
Function TritonPi2#(r)
y2=(2*r-Sqr(2*r^2))/2
For x=0 To 2*r
   For y = 0 To y2
      abst#=Sqr((x-r)*(x-r)+(y-r)*(y-r))
      If abst# <= r Then a# = a + 1
   Next
Next
Return 2+(4*a/r^2)
End Function