The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.
B-DNA has spirals in phi proportions
DNA in the cell appears as a double-stranded helix referred to as B-DNA.This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.
The DNA cross-section is based on Phi
Dr. Robert Langridge, known as the pioneer of molecular graphics, earned his Ph.D in Crystallography in 1957 with a dissertation on x-ray crystallographic, model building and computational studies of the structure of DNA. Over the next several decades he continued his work, which led to this 1985 photo of him:
In the photo is an image of the cross section of DNA, revealing a clear 10-sided geometry, the foundation of a decagon.
A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon.
The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!
This decagon-based nature of the DNA cross section was independently recognized by Dr. Stephen Marquardt. His research on human facial attractiveness led him to discover the relationship of the golden ratio to both the decagon structures found in both DNA and in the “Marquardt Beauty Mask” he created which provides an archetype to understanding human facial beauty.
His work describes Phi in 2D to show the pentagon and decagon as it relates to DNA, and extends that to “Making the Mask” to reveal a:
“complex of forty two (42) “secondary” Golden Decagon Matrices, which are exactly the same shape as the Primary Golden Decagon Matrix but smaller by various multiples of phi, are mathematically and geometrically uniquely positioned in the Primary (or framework) Golden Decagon Matrix. It is these forty two (42) Secondary Golden Decagon Matrices which ultimately form the various components of the face.”
The transformation from decagon to the Beauty Mask is discussed on this site at “Facial Analysis and the Marquardt Beauty Mask” and on Dr. Marquardt’s site at BeautyAnalysis.com.