#newton iteration for finding sqrt(2)
#parameters x = starting value
#           error = error tolerance in the approximation
#usage  newtonWhile(3.1, 0.00001)

#to get more digits use options(digits=15)


newtonWhile = function(x, error){   #function body start
                                    #do the first iteration, compute error
   x1 = 0.5*(x + 2/x)
   delta = abs( x1 - x )
   cat( "first delta = " , delta , "\n")

   x = x1                          
   
   while (delta > error){           #while starts
      oldx = x
      x = 0.5*(x + 2/x)
      delta = abs( x - oldx )
   }                              #while ends  

   print(x)
   cat( "last delta = " , delta , "\n")
}                                  #funtion body ends