# Sarah and the Fibonacci Sequence

My name is Sarah, and I’m a Secondary Math Education major. My favorite subcategory of math is the Fibonacci Sequence. This awesome set of numbers appears in the oddest places in mathematics, like in the Golden Ratio, talking about how trees branch, or sunflower seeds spiral in a flower. I’ve written and presented lessons to students about the Fibonacci sequence, and had the focus be on how the numbers show up outside of mathematics. What I don’t tell my students is that it has a lot of applications inside of mathematics, and I still come across new applications on a regular basis.

You can read more about the Fibonacci sequence on this fairly extensive Wikipedia article: Fibonacci Numbers

Also, here’s some information about the visual cousin of the sequence, called the Fibonacci spiral, or the golden spiral: Golden Spiral

The most famous part equation that is associated with this sequence is fairly simple: $F_n=F_{n-1}+F_{n-2}$

So, we get the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21….

My favorite part about the Fibonacci Sequence is that it pops up just about everywhere, and the numbers can be used in many different fields outside of pure mathematics. This makes the math more accessible and fun for students who may not take an interest otherwise.

## 5 thoughts on “Sarah and the Fibonacci Sequence”

1. grantrosandick

Cool post. This sequence is pretty incredible. It is strange how it pops up in many places outside of mathematics. That is very strange to me. I guess if I had a question about the Fibonacci Sequence it would be where it was first discovered. What sort of topics were being studied when this sequence was discovered?

It’s also great that you are finding this outside of pure mathematics, especially as a teacher. So many times students of math will ask when they need to use this in their life. Now you have an answer.

2. Jordan

I too enjoy the wonders of the Fibonacci Sequence as I am writing a paper about it at this moment. My favorite application of this sequence is in nature. I also find it fascinating that the golden ratio can be found in man-made structures thousands of years ago.

3. lukewarren

I really like the Fibonacci numbers interesting as well. Especially how they are connected to the golden ratio, which shows up in all sorts of places. It was also cool to me during the Euclidean algorithm lab how the GCD of two neighboring Fibonacci numbers is 1.

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