Have you ever pulled the petals off of a daisy? If you looked closely at the center, you would have seen that it is not solid, but made up of sets of spirals radiating out from the center. And it’s not just daisies. If you look at the bottom of a pinecone, it has the same kinds of spirals. Instead of going around and around in a circle, they spread out — like fireworks. To understand the spirals in pinecones, daisies, pineapples, and many other things in nature, we can look to the mathematician Leonardo Pisano, who is better known as Fibonacci (Fib-o-nawch-ee).
Fibonacci was born in Pisa, Italy, around 1170 and was educated in North Africa. As a child, he was encouraged to study accounting, and he recognized the enormous advantages of the mathematical systems in use there. Later in his life, he would introduce Arabic Numerals (Hindu-Arabic numerals) to the Western world. In a published work in 1202, Liber acaci, he advocated the use of these numerals, explained the use of zero, provided ways to convert between currencies and different measurements, and described how to calculate interest. One section of this book also led to the introduction of what are called the Fibonacci numbers and the Fibonacci sequence, and it is this contribution for which he is best remembered today.
Fibonacci posed a famous mathematical puzzle: “A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?” (Liber abbaci, pp. 283-284)
The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 … — a pattern of counting where each number is the sum of the previous two. Rabbits don’t actually breed as Fibonacci hypothesized, but his sequence still appears frequently in nature, as it appears to capture an aspect of growth. You can find it, for example, in the turns of natural spirals, in plants … and in the family tree of bees. One of the beauties of the Fibonacci sequence is that the series is evident all over the natural world. Petal arrangements in flowers, the ordering of leaves in plants, the shell of the nautilus, the DNA molecule and even hurricanes show patterns that correspond to the sequence.
The sequence also is closely related to a number called the golden ratio and, in addition to being prevalent in nature, this type of system is used widely in computer data storage and processing.
Which brings me to Fibonacci Day — a celebration that recognizes the importance and value of Fibonacci’s contributions to mathematics. This annual holiday takes place on November 23 — 11-23 — which corresponds to a portion of the first numbers in Fibonacci’s famous sequence. There are many creative ways people mark the event. Here are just a few ideas to get you started:
- A number of fruits and vegetables, like cauliflower and pineapples, display the Fibonacci series — incorporate them in your meals to celebrate this mathematical holiday.
- Build a Fibonacci LEGO Garden.
- Bake Fibonacci-themed spiral cookies or a Fibonacci stromboli.
- Where Math Meets Poetry: compose a Fibonacci poem.
- Trace a bee’s family tree.
- Learn more about sequences on Math TV.
For further information, visit: The life and numbers of Fibonacci