Open In App

GFact | Finding nth Fibonacci Number using Golden Ratio

Improve
Improve
Like Article
Like
Save
Share
Report
We have discussed different methods to find nth Fibonacci Number. Following is another mathematically correct way to find the same. nth Fibonacci Number :  F(n) = \left \lfloor \frac{\varphi^n}{\sqrt5} + \frac{1}{2} \right \rfloor, n >= 0 Here φ is golden ratio with value as (\sqrt 5+1)/2 The above formula seems to be good for finding nth Fibonacci Number in O(Logn) time as integer power of a number can be calculated in O(Logn) time. But this solution doesn’t work practically because φ is stored as a floating point number and when we calculate powers of φ, important bits may be lost in the process and we may get incorrect answer. References: https://www.youtube.com/watch?v=-EQTVuAhSFY http://en.wikipedia.org/wiki/Fibonacci_number

Last Updated : 17 Oct, 2023
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads