# How far can you go with Fibonacci?

Thursday 9th January 2020

I am fascinated by the Fibonacci sequence - something to do with it being recursive and the tendency for the common ratio between terms to become the golden ratio.

My favourite Fibonacci fact is the link between miles and kilometres and how it can be used to help make conversions - if I want to convert kilometres to miles, I just need to think of the previous term in the sequence et voila! For example, 5km is equal to 3 miles.

 Number of miles‌ Number of kilometres‌ 1 1 2 3 5 8 13 21 ‌Number of miles ‌Number of kilometres

If I want to convert miles to kilometres, then I think of the next term in the Fibonacci sequence - so 5 miles is 8 km

One of the reasons I love this is because I only realised this was true a few years ago and yet it is so obvious that this would work, I just hadn’t made the link before.

As Fibonacci now needs to be known for GCSE and students need to know the conversion between miles and km this might be another way to introduce the sequence and its use to your students.