Fletcher Hays

2022-06-20

The Fibonacci sequence is very well known, and is often explained with a story about how many rabbits there are after $n$ generations if they each produce a new pair every generation. Is there any other reason you would care about the Fibonacci sequence?

g2joey15

Perhaps it's not an entirely practical application, but Fibonacci numbers can be used to convert from miles to kilometers and vice versa:
Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No kidding – there are 8 kilometers in 5 miles. To convert back just read the result from the other end - there are 5 miles in 8 km!
But why does it work?
Fibonacci numbers have a property that the ratio of two consecutive numbers tends to the Golden ratio as numbers get bigger and bigger. The Golden ratio is a number and it happens to be approximately 1.618.
Coincidentally, there are 1.609 kilometers in a mile, which is within 0.5% of the Golden ratio.

Semaj Christian

It isn't exactly an application as such, but the upper bound of the size of a subtree in a Fibonacci heap whose root is a node with degree $k$ is ${F}_{k+2}$ where ${F}_{n}$ is the ${n}^{th}$ Fibonacci number.