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.

1:1.618

For many, working and living in the same space presents a challenge to motivation and focus. Without distance or space to temporarily take away the forgiving environment of home, more than few of us find the distractions a barrier to uninterrupted work. But then there is another side to having a place apart and that’s those occasions we yearn for space that takes us away from everything, a place where we can sit watching the wheels go round, answering the questions we ask ourselves.

Michael Pollan wrote a book in 1997 called A Place of My Own in which he recounts the process of designing and constructing a small one-room structure on his rural Connecticut property—a place in which he hoped to read, write and daydream. Though a confessed non-carpenter, Pollan built his ‘writer’s house’ with his own two hands. Not a task he approached lightly or with any sort of confidence, it was rather an endeavor that involved long thought and careful research, plus the help of a longtime architect friend.

A Place of My Own takes the reader through each phase of the project, from the germination of an idea thrown out by the friend-architect remodeling Pollan’s home. Looking out from an unfinished second floor window to the slope, woods and meadow beyond, the architect felt the view needed a focus and the best bet would be a small structure build on the same axis as house, garden and meadow. At the same time Pollan had been thinking of a small hut or room set apart where he could do his writing. Next came research on the marriage of architecture and nature, on the question of selecting a site, and then a study of sketches from the architect’s standpoint.

From the initial concept the project was never meant to be large, complicated or expensive. A big part of that was Pollan’s desire to build the structure himself, a decision that required more than anything simplicity. But to make a long story short, this dream of Pollan’s was eventually realized, designed by his friend, but built by Pollan at an ultimate cost of $125 per square foot.

One part of the story is particularly interesting and involves a system unfamiliar to me before reading Pollan’s book. There is a mathematical formula of sorts known as the Golden Section, a famous mystical sequence of numbers illustrating that the ratio 1:1.618 occurs again and again in both architecture and nature. It can be seen in the elevation of the Parthenon and in the wings of a butterfly; found in the facade of Notre-Dame, it is also evident in the spiral of a seashell. In sizing the ground plan of Pollan’s one-room writer’s house, the architect along with Pollan 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, a span measuring six feet, to which was added the depth of two feet for bookshelves on each end. This gave them the width of the room. Using the Golden Section, the architect then multiplied that length (eight feet) by the factor 1.618, coming up with 12.9. He then sketched a rectangle eight feet by thirteen indicating the final measurements of the room.

Charles R. Meyer, Pollan’s architect has this to say about the Golden Section: “The Golden Section is a bridge joining architecture and nature. The same proportioning system that works in buildings also shows up in trees, leaves, seashells and sunflowers, as well as the human body. It’s everywhere.” Both Frank Lloyd Wright and Le Corbusier were faithful to the principle in their work.

In the Lamplight

Unusual in my often laid back life here at the beach, but this Saturday has been a non-stop day, leaving me little time to muse upon those things I most love. No thought for ocean scenery, for local color or fountain pens; no spare seconds for book browsing or dabbling in ink.

The usual pattern of my days more often than not allows me to read throughout the morning, corral some thoughts, and give most of the afternoon to writing or researching a topic relevant to a story or other writing project on my work table. That wasn’t in the cards today, and too much of the day has been taken up with issues that even now in this quiet solitary corner dominate my thoughts and scare off the quiet contemplation I am used to.

With a minimum of planning and too little to color in the details, here is a list of books that I have enjoyed, books that have not been previously reviewed or commented on at any length in past pages of this blog. In most cases the books listed below are titles I have either read more than once, or would happily do so.

Some exceptional books that have enlivened my love of reading.

NOVELS:

1. The Voyage by Philip Caputo

2. The Amazing Adventures of Kavalier & Clay by Michael Chabon

3. The Missing by Tim Gautreaux

NON-FICTION:

1. The Botany of Desire by Michael Pollan

2. The Gifts of the Jews by Thomas Cahill

3. The Elements of Style by William Strunk & E.B. White

SHORT STORIES:

1. Flannery O’Connor, The Complete Stories by Flannery O’Connor

2. Things You Should Know, a Collection by A.M. Homes

3. “All Boy” by Lori Ostlund in Best American Short Stories 2010

POETRY:

1. Bone Palace Ballet: New Poems by Charles Bukowski

2. ten poems to change your life, compilation and commentary by Roger Housden

3. Bashô, The Complete Haiku by Matsuo Bashô, translated by Jane Reichhold

MYSTERY OR SUSPENSE:

1. Farewell My Lovely by Raymond Chandler

2. Burning Angel by James Lee Burke

3. The Power of the Dog by Don Winslow

To sit alone in the lamplight with a book spread out before you and to hold intimate converse with men of unseen generations—such is a pleasure beyond compare. —Yoshida Kenkô, Essays in Idleness (1340)