Fibonacci Spirals

These spirals are constructed by adding squares of successive sizes in the Fibonacci series: 1, 1, 2, 3, 5, ... As the figure grows, it ever more closely approximates the dimensions of a golden rectangle and the ratio of the length to the width of the whole converges on φ, 1.6180339887498948... But, because φ is irrational, no ratio of integers can equal it; the shape approaches that of a perfect golden rectangle but never gets there. Instead, the ratio of length to width alternates between being less than and greater than φ: 1.000, 2.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618 ...

The first stone spiral I made was an emblem for the travertine surround of the new bathtub; making it allowed me to participate in the construction of the additions to the Flying Bridge. The largest square is Peninsular gneiss, the 3 billion-year-old tectonic sled India used to speed away from Gondwanaland and collide with the Eurasian plate. The next largest square to its left is Labradorite, the magic feldspar from Madagascar also used in the Cross for Saint Brendan, the Stone Garden, and most of the works submitted to the DIAA 12x12 exhibition.

I have also tried my hand at hawking these spirals at the Stonington Farmer's Market. That enterprise generated many more interesting conversations than sales. Given that most of those shopping at the market are wealthy senior "aways", my usual spiel capitalized on the fact that many of them had grandchildren. I would tell them that the spirals are excellent additions to a grandparent's coffee table. The stone squares beckon grandchildren's attention to the mathematics of their relationships. And the stone itself invites their curiosity about mineralogy; the stones provide an opportunity to begin to learn about gneiss and granite, feldspar and biotite, orthoclase and plagioclase, and etcetera. In other words, the spirals tug at children's imagination both toward the abstract and the concrete, both sky and earth.