Matematické Fórum

var L,d,h: Extended;
function Newton(L,d:Extended):Extended;
var a,b,c,wk,wk1,tol:Extended;
begin
  tol := 1e-10;
  c := L/d;
  if c>1 then
  begin
    a := 1+ln(c*(1+61*ln(c)/61));
    b := sqrt(6*(c-1));
    if a<b then
      wk := a
    else
      wk := b;
    a := (exp(wk)-exp(-wk))/(2*wk)-c;                      //f(wk)
    b := (exp(wk)*(wk-1)+exp(-wk)*(wk+1))/(2*wk*wk);       //f'(wk)
    wk1 := wk-a/b;                                         //novy (presnejsi) koren
    while abs(wk1-wk)>tol do
    begin
      wk := wk1;
      a := (exp(wk)-exp(-wk))/(2*wk)-c;
      b := (exp(wk)*(wk-1)+exp(-wk)*(wk+1))/(2*wk*wk);
      wk1 := wk-a/b;
    end;
    Result := d*((exp(wk1)+exp(-wk1))/2-1)/(2*wk1);
  end
  else
    if c=1 then
      Result := 0
    else
      Result := -1;
end;

begin
  Write('Zadej vzdalenost bodu: ');
  ReadLn(d);
  Write('Zadej delku lana: ');
  ReadLn(L);
  h := Newton(L,d);
  WriteLn;
  if h<>-1 then
    WriteLn('Pruhyb lana je: ',Format('%8.2f',[h]))
  else
     WriteLn('Delka lana je kratsi nez vzdalenost bodu');    
  ReadLn;
end.