ECO-Essays are daily 2.5-minute short programs, each combining music and nature sounds uniquely matched to a spoken essay. They are intended to be aired on public radio stations nationwide at least twice a day, preferably right after "Morning Edition" and "All Things Considered."
"She loves me, she loves me not, she loves me...." Surely you've picked petals off a daisy. But while your heart flutters, have you looked closely at the heart of a daisy--at what's left once you've finished plucking? Welcome to ECO-Essays--encouraging environmental awareness and responsibility.
Up close, the yellow middle of a daisy reveals unexpected structure. That yellow center of tightly packed florets contains two sets of spirals coiling out from its center: a clockwise and counterclockwise set. Such interlocking spirals abound in nature. You can see interlocking spirals on sunflowers, on the outside of pinecones, even on the dreaded prickly facade of pineapples. Indeed, nature is not discriminating: we see hypnotic spirals in both the beauty and the beast.
In nature, just as in our lives, moving from a qualitative impression to a quantitative view may lead to new discoveries. We've seen spirals in flora and fruit, but exactly how many spirals are there?
On a small pinecone you count 3 spirals in one direction, and 5 in the other. The pineapple has 8 and 13; the daisy 21 and 34. The big sunflower has a staggering 55 and 89. So, those counts are:
You ask, what's amazing about this list of numbers? Well, any number on that list is exactly the sum of the two previous numbers. Take 3, 5, and 8 (8 is 3 plus 5), or 13 (13 is 5 plus 8); 21 is 8 plus 13, and so on.
These numbers are called Fibonacci numbers, after the 13th-century Italian mathematician who first discovered them. Here, wild nature and number patterns reflect each other. So, the next time you're in the fruit section, count the spirals of a pineapple, verify the 8 and 13 counts. Feel the power of looking at our world in a deeper way.
Our writer was Williams College Professor Edward Burger, co-author of the forthcoming entertaining book and kit: "The Heart of Mathematics: An invitation to effective thinking" published by Springer-Verlag.