The Math of Flowers & Bees

Throughout history, one particular ratio for the length and width of rectangles has been determined to produce a shape pleasing to the eye. Named the Golden Ratio by the Greeks, the ratio of 1.61803 has fascinated scholars, scientists, architects, painters and musicians for centuries. In the world of mathematics, the numeric value is called phi, named for the Greek sculptor Phidias who used the ratio in finding the best proportions for his statues. 

The number is derived from something known as the Fibonacci Sequence—an arrangement of numbers wherein each succeeding number is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…). This sequence forms the basis for the Golden Ratio of 1.618—a proportion which recurs with amazing consistency throughout the natural world.

Without benefit of a strong background in mathematics, this phenomenon of numbers and nature didn’t come to my attention until recently, when I read Michael Pollan’s book, A Place of My Own, his account of building a small one-room writing space that he called a “shelter for daydreams.” In sizing the ground plan for Pollan’s studio, the architect determined that the desk should run the length of the front wall. To get an idea of dimensions Pollan extended his arms out to the side, making a span of six feet, then added a depth of two feet for bookshelves on each end. This gave them the room’s width. Using the Golden Ratio, the architect multiplied that length of eight feet by the factor 1.618, coming up with 12.9. In this way he determined the final measurements of the room—a rectangle of eight by thirteen feet.

Nature’s perfect number also fits snugly into this Golden Mean. Odd as it seems to equate math with flowers, we can see shapes determined by this formula in the heads of daisies and sunflowers, in pine cones, leaves and seashells. The shape and proportions of a dolphin’s body, the markings on a butterfly or moth, as well as the facial features of tigers and koala bears all fall into line with the Golden Ratio. If you divide the number of female honey bees by the number of male honey bees in any given hive, you will get 1.618—the Golden Ratio. While there are arguments against it, many believe that for centuries great architecture has been influenced by the Golden Ratio. Some say that the Pyramids of Egypt reflect the Golden Ratio, that the Greeks used it in building the Parthenon, and the French in Notre Dame. It has figured in the thought and painting of Leonardo da Vinci and Salvador Dali, the architecture of Frank Lloyd Wright and Le Corbusier, as well as the music of Chopin.