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You don't need to use a root solver. If you represent numbers as "a + b sqrt(5)" you can do algebra directly in that space.
by panic 10y ago
You don't need to use a root solver. If you represent numbers as "a + b sqrt(5)" you can do algebra directly in that space.
- tanderson92 10y agoI take it you are making a joke? Heh. Otherwise, I'd point out that any result where you ultimately need to use Fibonacci(n) as an actual integer, you can't represent it as an algebraic combination of "sqrt(5)".
- panic 10y agoNo joke! See this thread: https://news.ycombinator.com/item?id=11561336 https://news.ycombinator.com/item?id=11561336 for some real-life implementations of this technique. Since the Fibonacci numbers are integers, at the end of your computation you'll get a number like "a + 0 sqrt(5)". Then you can just take the "a" part.
- tanderson92 10y agoAh! I see what you're saying. Thank for the link, that is a clever approach.