Recursive Formula

Here is a recursive version of this:

• if guess*guess nearly equals N then Newton( N, guess ) = guess
• otherwise, Newton( N, guess ) = Newton( N, N/(2*guess) + guess/2 )

Recall that

guess*guess nearly equals N

can be rearranged into

N/(guess*guess) nearly = 1.0

which can be rearranged into

| N / (guess*guess) - 1.0 | < smallValue

where the vertical bars mean "absolute value".