Fibonacci Day

 

Biblioteca Ambrosiana, Milan*

November 23, which is 11/23 in month/day notation, always brings to mind the Fibonacci Numbers. I think some people even celebrate Fibonacci Day, though I haven't seen it get as much traction as Pi Day, which is March 14 or 3.14.

The Fibonacci Numbers are 1, 1, 2, 3, 5, 8, 13, 21 and so on, a sequence begun with 1, 1 and in which each succeding term is found by adding the previous two numbers. For example, the next number above would be 34, since 13+21=34.

As we'll see in a moment, this number sequence shows up in the natural world and in other places around us, which has made them popular, but first I want to spent a moment on their name and origin.

Fibonacci Memorial - Camposanto - Pisa, Italy

Because the number sequence 1, 1, 2, 3, 5, 8 . . . is called the Fibonacci Sequence, it is often thought that Fibonacci developed it. This is not true; it was known long before his time, going back well over a thousand years before his birth. Fibonacci did include a problem in his work Liber abbaci (Book of Calculating) that resulted in this number sequence. It was here that it became popularized and is why it bears his name.

Fibonacci Memorial (left-most sculpture) - Camposanto - Pisa, Italy

Despite knowing about this sequence for decades, what I didn't realize until recently is that Fibonacci's name was nearly lost in the mists of time. In fact, though he lived from about 1170AD to about 1250AD, he wasn't known as Fibonacci until 1838. His name was Leonardo, and he was from Pisa, so he was called Leonardo of Pisa (sort of like Leonardo da Vinci) or Leonardo Pisano. Fibonacci is a contraction of the term filius Bonacci ("son of Bonacci" or "of the house of Bonacci") that Leonardo refers to himself as in his book. Professor Keith Devlin, of Stanford University, went in search of Fibonacci's life and legacy beginning in about 2010, a journey that lasted about a decade and resulted in three very iteresting books: The Man of Numbers, Finding Fibonacci, and Leonardo and Steve - each of which I highly recommend if you want to learn more about about Fibonacci and the profound and ongoing impact of his work. For purposes of this post, we will not turn our attention to Fibonacci Numbers around us.

This number sequence often (though not always) shows up in the number of flower petals (or tepals).

The cala lily has 1 spathe.

The day lily had 3 petals and 3 sepals. (The three tepals with purple and yellow are petals; the other white tepals are sepals. Little did you know there would be botany terminology in this post!)

Many flowers display the "Fibonacci Five," as I like to call it. Here are a few examples:

Here we have 8 petals..

Daisies often display 13, 21, 34, or 55 petails; the daisy below has 21:

It's not just numbers of tepals that display Fibonacci Numbers but also numbers of spirals in natural objects. When I first learned this many years ago, I wasn't sure exactly what it was that I was supposed to be counting in order to find these numbers, so I'm including two explanatory photos below this pinecone, which has 8 spirals if you count the going clockwise and 13 spirals if you count them going counter-clockwise. Note that 8 and 13 are consecutive Fibonacci Numbers.

Pineapples too generally have a number of spirals that are Fibonacci. There are three spirals on a pineapple, and each of the three Fibonacci Numbers is consecutive.

And it's not just the amount of spirals that turn out to be Fiboacci. There are alsp spiral shapes that have the Fibonacci Numbers hidden in them.

The shape of the Chambered Nautilaus shell above can be modeled well by using the Fibonacci Numbers to create a grid - staritng with a square of side-length 1, then another square side-length one, and then a square next to those with side-length 2 and so on as shown below - and then spiraling out from the original square to the outermost square:

And, here are the Fibonacci Numbers 5, 8, and 13 showing up in an octave on a keyboard:

Whatever November 23 holds in store for you, I hope it's a happy Fibonacci Day!

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*The picture at the top of this post is of Milan's Biblioteca Ambrosiana. In their collection is a manuscript copy of the Liber abbaci. During a visit to Italy in autumn 2024 I consulted their copy, and I found it to be a deeply moving experience to handle an 800-year-old manuscript, a book that introduced the number system we used today into Europe in a way that merchants and others could make use of it. I would rank the importance of this book near the importance of the printing press for the impact it has had in ushering in the modern age.