Question

Hi, How is finding the square root by successive averaging related to finding a fixed point? It's from the first video lecture, but I am finding it hard to understand.

Answer 1

The value guess = sqrt(x) is a fixed point of (average guess (/ x guess)))
since x/sqrt(x) = sqrt(x).

Answer 2

Maybe it makes more sense this way: You want to find the square root of any number x. If you look at the function avg(guess, x/guess), you'll see that only if your guess=sqrt(x), does the function valuate as avg(guess, x/guess)=guess. So your parameter is "guess" and the value of the function is also "guess", which is the definition of a fixed point.

Bottom line you were not looking for a fixed point, but for a function for which the fixed point is the thing you were looking for and that is the avg function above.

Let me know if this was helpful to you.