%!PS
%%BoundingBox: 10 40 600 630
/doos { newpath dup 3 2 roll dup 6 1 roll exch moveto
        3 2 roll dup 4 1 roll exch lineto
        dup 4 1 roll lineto  exch lineto  closepath stroke } def
%
% 10 40 600 630 doos
%
/Times-Roman findfont 0.13 scalefont setfont
%
0 20 translate  150 150 scale
0.006 setlinewidth
%
% X-axis and Y-axis:
newpath 0.2 0.27 moveto 3.75 0 rlineto
        0.77 0.2 moveto 0 3.5 rlineto  stroke
%
0.77 0.27 translate
%
% Start & increments:
/x -0.5 def   /dx { x /x x 0.01 add def } def
%
/fun { dup 0.5 eq { pop 1000 } { dup  1 exch 2 mul sub dup mul
                                 exch dup mul exch div } ifelse } def
newpath dx dup fun moveto
  361 { dx dup fun dup 3.3 gt { moveto }{ lineto } ifelse } repeat stroke
%
0.002 setlinewidth newpath
%
/Times-Roman findfont 0.10 scalefont setfont
%
2.5 -0.08 moveto (x) show
-0.08 1.8 moveto (y) show
-0.08 -0.08 moveto (O) show
0.8 2.5 moveto (y\50x\51 = x^2/\50 1-2.x\51^2) show
%
newpath -0.5 0.25 moveto 3.5 0 rlineto stroke
-0.15 0.27 moveto (1/4) show
newpath 0.5 0 moveto 0 3.5 rlineto stroke
0.45 -0.08 moveto (1/2) show
newpath 0.25 0 moveto 0 0.25 rlineto stroke
0.20 -0.08 moveto (1/4) show
%
% DANGEROUS POINTS
%
% Function  y = sqrt(w)  with Newton-Rhapson.
%
% Theory:  y(n+1) = y(n) - f(y(n))/f'(y(n))
%
% Here: y = sqrt(w)  or  y^2 = w . Take f(y) = y^2 - w , then  f'(y) = 2.y
% ==>   y(n+1) = y(n) - (y(n)^2 - w)/(2.y(n)) = y(n) - y(n)/2 + w/y(n)/2
%
% Conclusion:  y(n+1) = 1/2.( y(n) + w / y(n) )
%              --------------------------------
/wortel
{ /y 0.5 def  /w exch def  w 0 le { /y 0 def }
{ 7 { /y  y w y div add 0.5 mul  def } repeat } ifelse y } def
%
/plus { wortel dup 2 mul 1 add div } def
/min  { wortel dup 2 mul 1 sub dup 0 le { pop 1000 } { div } ifelse } def
/trekplus { newpath xp plus 0 moveto 0 xp dup 3.5 gt { pop 3.5 } if
            rlineto stroke } def
/trekmin { newpath xp min 0 moveto 0 xp dup 3.5 gt { pop 3.5 } if
           rlineto stroke } def
%
/x0 0.5 def
/xp x0 def trekplus trekmin
%
/xp x0 plus def trekplus trekmin
/xp x0 min  def trekplus trekmin
%
/xp x0 plus plus def trekplus trekmin
/xp x0 plus min  def trekplus trekmin
/xp x0 min  plus def trekplus trekmin
/xp x0 min  min  def trekplus trekmin
%
/xp x0 plus plus plus def trekplus trekmin
/xp x0 plus plus min  def trekplus trekmin
/xp x0 plus min  plus def trekplus trekmin
/xp x0 plus min  min  def trekplus trekmin
/xp x0 min  plus plus def trekplus trekmin
/xp x0 min  plus min  def trekplus trekmin
/xp x0 min  min  plus def trekplus trekmin
/xp x0 min  min  min  def trekplus trekmin
%
% program funktie2;
%
% var
%   k : byte;
%   x : double;
%
% begin
%   for k := 5 to 14 do
%   begin
%     x := 1/(2+2*cos(pi*k/16));
%     Writeln(x:9:4,' ',0,' 0.01 0 360 arc closepath fill')
%   end;
% end.
%
   0.3214 0 0.015 0 360 arc closepath fill
   0.3616 0 0.015 0 360 arc closepath fill
   0.4184 0 0.015 0 360 arc closepath fill
   0.5000 0 0.015 0 360 arc closepath fill
   0.6212 0 0.015 0 360 arc closepath fill
   0.8100 0 0.015 0 360 arc closepath fill
   1.1250 0 0.015 0 360 arc closepath fill
   1.7071 0 0.015 0 360 arc closepath fill
   2.9668 0 0.015 0 360 arc closepath fill
   6.5685 0 0.015 0 360 arc closepath fill
%
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