Monday, October 3, 2011
THE BEAUTY OF THE FIBONACCI MYSTIQUE
To Bee Fibonacci or Not to Bee, Jamestown, NC
Fibonacci Floret Spirals, Jamestown, NC
Fibonacci Petals, Jamestown, NC
During the European Renaissance mathematics and music were called perfect arts. As man began to evolve into the higher realms of these disciplines I believe that we also became closer to the ultimate creator of this universe. Some folks would argue that science will ultimately have an answer to all of life’s mysteries that will exclude the existence of a divine mind that is the source of all creation. Others like Francis Collins who headed the Human Genome Project that sequenced the DNA code of life, has found that a higher understanding of our world only strengthens their faith in God. He introduces his book, The Language of God, with the observation that “science’s domain is to explore nature. God’s domain is in the spiritual world, a realm not possible to explore with the tools and language of science. It must be examined with the heart, the mind, and the soul—and the mind must find a way to embrace both realms”. Collins writes, “How marvelous and intricate life turns out to be! How deeply satisfying is the digital elegance of DNA! How aesthetically appealing and artistically sublime are the components of living things…For those who believe in God, there are reasons now to be more in awe, not less”.
I awoke to a bright and cool early autumn October morning to discover that Shasta Daisies had blossomed overnight after a soaking rain. So, I retreated out into my backyard after a warm cup of coffee with my trusty digital camera in hand to document the event. It was only after I downloaded and cropped the images on my computer that I witnessed the startling, organized, and opposing spirals of tightly-packed tiny florets in the center of the blooms. It seemed more than a bit of serendipity that only yesterday as I was writing a short blog on shapes and forms that I had remembered a college mathematics class where we worked with the Fibonacci sequence of integer numbers. For starters, they relate to an ancient Greek mathematical proportion of 1.618034 that appeals to both the intellect and the eye and is achieved as you go further out in the sequence to calculate the ratio of adjacent terms. This became the famous ratio called The Golden Mean of Euclid and Aristotle, the divine proportion of Leonardo daVinci (Mona Lisa’s face), and has since been valued as the most beautiful proportion to the human eye. The golden ratio is integral to the horizontal and vertical beams of the Christian cross. The visually pleasing golden rectangle the Greeks derived had a proportion where the length was 1.618034 and the width was 1.0 and this shape became the basis for their art and architecture. This esthetic of thirds was adopted by the great Renaissance artists and remains to this day as a visually pleasing proportion for cropping land and seascape images.
If I learned nothing more in my pursuit of a mathematics degree, it was that the higher I advanced in successively more complicated studies, the more I began to appreciate the beautiful structure of our universe and the world around me. The Fibonacci sequence that has application in a variety of studies reinforced that concept for me—especially when found in nature. These numbers can be created by beginning with 0 and 1 and then adding the previous two numbers in the sequence to arrive at the next one. The number of petals on many flowers, for instance, can be associated with one of the Fibonacci numbers. Most daisies like the ones blooming in my backyard have 34, 55 or 89 petals; the 9th, 10th and 11th Fibonacci numbers. There can be 21 spirals going to the left and 34 to the right. Four leaf clovers are rare because four isn’t a Fibonacci number. But it is in the center of the Daisy I photographed that incredible order is observed to mathematical precision. If you start at the very center or the capitulum, you will find one individual floret and then they spiral out in rows of Fibonacci numbers of 2, 3, 5, 8, 13, 21, 34, etc. The number of curving clockwise and counterclockwise ordered spirals can be found in the seeds of sunflowers, bracts of pine cones, and scales of pineapples. Golden spirals can be found in chambered nautilus sea shells and the curve of waves. Leaves on the stem of a flower or a tree branch often grow in a helical pattern as the branch grows outward. A pear tree, for example, will have 8 leaves and 3 turns along the branch—both numbers are Fibonacci numbers. The number of the sets of seed spirals on a sunflower will always be consecutive like 21 and 34 or 55 and 89 to further confirm the beautiful Fibonacci mystique.