Understanding Fibonacci and the Golden Ratio via perfect simulation

11/08/2016 - 12:15pm
11/08/2016 - 1:10pm
Mark Huber (CMC)

The Fibonacci sequence has long been studied for its wonderful properties, including the fact that the ratio of successive terms approaches the Golden Ratio. In order to understand why this happens from a probabilistic perspective, I'll build a computer experiment over n different {0,1} random variables where the probability of the outcome being true is the n-th Fibonacci number divided by 2^n. By extending the probability distribution to infinite graphs, it becomes possible to find this limit of successive terms for large n as well as rederive the classic formula for the n-th Fibonacci number in terms of the Golden Ratio.

Millikan 2099, Pomona College

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