0      1     1     2     3     5     8     13      21      34      55      89      144     233      377

Math?  Really, must we talk about math?  What could this have to do with Tyler Arboretum or nature?  Well, let’s take just a moment and see if we can find math in nature, and maybe have fun at the same time.  Yes, I put the words ‘math’ and ‘fun’ in the same sentence.

The numbers above have a pattern, which is simply starting with zero and adding the next consecutive number (1) to it to get a result of 1.  Then keep going to add 1+1 to get 2, then 1+2 =3, then 2+3=5 and so on.  Okay, that’s easy enough.  We have a list of numbers that have a pattern and can go on forever.  The man who identified this sequence was Leonardo of Pisa, a mathematician born in the 12th century who was known as ‘Master Fibonacci’.

Now, let’s look at how plants grow.  It doesn’t make sense for plants to stack leaves over each other since that would block sunlight, and limit water’s ability to travel down the stem to reach the roots.  When a plant produces its leaves in a spiral up the stem, it allows for optimal sunlight and water dispersal.  By the time a leaf is directly over another leaf, it is far enough up the stem to not interfere with the leaf directly below it.  If you count these leaves as they spiral up the stem, the overlapping leaf will be the 3rd (elm), 5th (cherry) or 8th (pear).  Remember to start with 0, and count up from there.  Let’s take this idea of spirals further.

beautiful leaf


Take a look at the coneflower pictured below.  At this angle, you can easily notice the spiral pattern in the center.  What about the dahlia?  If you were to count the spiraling petals from left to right, you would get one of the numbers listed above, in this case 8.  Count in the opposite direction and you will get another Fibonacci number.  Now look at a pinecone and count the individual bracts as they spiral towards the tip.  Going in one direction, you will see that the bracts slope upwards gradually.  Going in the opposite direction the slope rises more steeply.  But the sum of each path of spiraling bracts results in a Fibonacci number.


flower collage


Of course this numbering is not always displayed in nature, but you will find it more than you might think.  Look at the seeds in a sunflower.  They are tightly packed in a spiral, and if you count them, you will see Fibonacci numbers going in each direction – 55 going clockwise, and either 34 or 89 going counter clockwise.  Look at a pineapple, an artichoke, water lilies, carnations.  Over and over, you will find the same numbers.

Even if you look at flowers which do not form spirals, you will often find the total number of petals to be a Fibonacci number.  Iris have 3 petals, phlox have 5, delphiniums have 8, cineraria have 13 and black-eyed susans have 21.  The list goes on.  

Whether you are in your backyard or at Tyler, look closely and you will start seeing these spirals, and finding these petal counts.  Not to be left out, you will also see shapes like circles (berries or the rings of a tree), stars (sweetgum leaves or an apple core) and even squares (the square stem of a mint, or the seed capsule of Ludwigia alternifolia, commonly called seedbox – pictured below and found at Tyler).  While these shapes have nothing to do with Fibonacci, the kids in your life can seek out Fibonacci sequences or shapes, depending on their skill level while enjoying an outing at Tyler.  See?  Math can be fun!




Learn more about the Fibonacci sequence in nature.