• anonymous
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.
MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005
  • schrodinger
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  • anonymous
The value guess = sqrt(x) is a fixed point of (average guess (/ x guess))) since x/sqrt(x) = sqrt(x).
  • anonymous
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.

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