Back to Top
  /  Blog  /  Fibonacci and the Golden Ratio

Fibonacci and the Golden Ratio

This short film is beautifully crafted in CGI by Cristobal Vila and illustrates the Fibonacci sequence, as well as Delaunay Triangulation and Voronoi Tessellations. It begins with showing how the nautilus builds the chambers of its shell to accommodate its body’s growth, and moves on to the sunflower and the dragonfly.

My friend, Briar Cook made me aware of this film and it is ironic that I was first made aware of the name Fibonacci by her father, Alleyne, our gardening mentor. Many years ago, Alleyne explained the mathematics behind the pattern that sunflower seeds form as they grow in the face of the flower. Of course, mother nature figured it out first, and then Fibonacci found a way to explain it.

Fibonacci, or Leonardo of Pisa was an Italian mathematician from c. 1170 – 1250 and is credited for introducing the sequence to the Western world in his Liber Abaci. Each number in the Fibonacci sequence is the sum of the previous two numbers starting with 0 and 1. The higher up the sequence, the closer two consecutive numbers divided by each other will equal the “Golden Ratio” of approximately 1 : 1.618…, or phi.

As the film illustrates, Mother nature has been using this formula to create beauty for centuries. Once identified, artists have been using the Golden Ratio to create a pleasing composition in painting and sculpture. In a painting, the Ratio could be as simple as the dimensions of the canvas, or more subtly as the dimensions of the focal point. For the sculptor, it could be used for a perfect base under a carving, or the subtle outside dimensions of a sculpture.

I recall my sculpting mentor mentioning the Golden Mean or Ratio many years ago and trying to explain it to me in order to create the most visually pleasing sculpture. However, the simplicity of Fibonacci’s sequence eluded the conversation. While I have intuitively attempted to create a pleasing composition with a good proportion ratio of width to height to depth, I think it would be interesting to do a series of pure abstract sculptures based more closely on the Golden Ratio.

Leave a reply