I have a close friend with whom I share dinner on a weekly basis. Two of our favorite restaurants hand us identifying numbers to carry to our table so servers can locate where to carry our orders. Analyzing these numbers is a pastime shared with the cashier assigning them to us, much to his or her astonishment and amusement. Is it a perfect square? Is it a prime? If not, how do I write it as a product of primes? Our discussion continues on the walk to our table and more than once we’ve expressed gratitude no one else is privy to the conversation.

Sometimes there are numbers that do interest mathematicians in a theoretical sense and also appeal to the general public. As an example, we have Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano (the same person with different appellations) to thank. Most mathematicians would not recognize any of these names. But all would be aware of the more familiar designation Fibonacci, an Italian mathematician who lived from roughly 1170 to 1250.

We owe Fibonacci a debt. He wrote a book

*Liber Abaci*(Book of Calculation) which advocated for the use of digits zero through nine and the place system where the rightmost digit counts ones, the next digit to the left counts 10s, the next 100s, and so forth. That is, he proposed the system we all use today. Better than counting knots on a rope or any of the other methods that have been proposed in antiquity. If you’re interested, en.wikipedia.org/wiki/Fibonacci is the Wikipedia link which discusses him in more detail and gives several references.

What’s of interest here is the Fibonacci sequence, that is, the following sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

How do you get these numbers, called Fibonacci numbers? Simple. Start with the 0 and the 1. The next number in the sequence is the sum of 0 and 1, that is, 1. Then add the last two numbers, 1 and 1, to get the next number 2. Then the last two, 1 and 2 to get 3, and so on forever and ever.

Not hard, right?

But who cares?

Well, these numbers appear in strange and unexpected places. For example, they occur in my book

*Murder By The Numbers*. But perhaps you were looking for something a bit less lethal. So here are a few areas in nature where you might look to find them.

- Examine a sunflower. The center includes seeds arranged in spiral patterns. Some point left and some right. Count them all. You should get a Fibonacci number. Then count the number pointing left and the number pointing right. Each of these numbers in a Fibonacci number. In fact they are two consecutive numbers of the sequence. Does that make sense?
- Notice that the bumps on a pineapple also are arranged as spirals. The number of them is a Fibonacci number.
- Check out trees. Follow a trunk up until it splits forming two points for further growth. The trunk keeps growing and produces a second branch for three growth paths. After a while the trunk and the first branch each produce a new branch for a total of five. Then the trunk, the first branch, and the second branch produce three more for a total of eight, and so on.
- Count the number of petals on a flower. It depends on the flower, but often this is a Fibonacci number.

There are many other examples and spending a little time with Google can uncover more.

If you divide a Fibonacci number by the one preceding it in the sequence, you will always get a number close to 1.6. As you do this with bigger and bigger Fibonacci numbers the ratio changes very little and seems to be getting closer and closer to a specific number. This number is called the “golden ratio” and it is responsible for some of the pleasure in our lives.

But that’s for another day.