Notes on Fibonacci series and Golden ratio

  1. Early known roots of Fibonacci series lie in Pingala (200 BC)
  2. Fibonacci numbers are attributed to Leonardo Bonacci of Pisa, Italy and are a number sequence where the previous two numbers are added to create the next number in the sequence; such as 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. This number sequence can be seen throughout nature as in the arrangements of seed spirals in a sunflower and the number of petals in many flowers.
  3. The ratio between two adjacent values approaches the Divine Proportion, or Golden Ratio known as Phi (pronounced fee) being the ratio of 1.618 to 1. This ratio also exists throughout nature. It can be seen in the increasing radii of the chambered nautilus and in the proportions of the human body.
  4. More significantly both Fibonacci numbers and the Golden Ratio can be found in the DNA of every cell in our bodies. Jean-Claude Perez discovered a DNA supracode controlling the self-organization of the nucleotide bases Thymine, Cytosine, Adenine and Guanine (T,C,A,G), which make up the steps in the double helix ladder of DNA. He discovered if you consider 144 contiguous nucleobases it results from 55 T bases and 89 C A G bases, all Fibonacci numbers. These resonances extend to the ratios of the Atomic Weights of the Bio-Atoms of Carbon, Oxygen, Nitrogen and Hydrogen that create the nucleotide bases of T C A G, such that the ratios of atomic weights in strands considered to be ‘junk DNA’, that is DNA which could not be translated into genetic information or related to known protein synthesis, were equal to Phi, the Golden Ration of 1.618. Thus, even within the basic building blocks of our bodies Fibonacci number sequences and Phi exists at a primal level. These and other personal insights led to understanding the fundamental frequency from which all subsequent therapeutic frequencies would be derived must be based upon a natural Fibonacci number.

And then there’s the essential character of the…

And then there’s the essential character of the universe. It is this mechanical system of laws and particles and principles. Utterly devoid of a moral or personal agenda, and instead being an expression of mathematical interactions. Now that could be the signature of a math-centric geek god. But if the cosmos is impersonal and indifferent, that removes any character from creation. We don’t need a god to explain it. Just a big textbook.

-Glyn Williams

Reproduced from

The ultimate abstraction takes place in mathematics where…

The ultimate abstraction takes place in mathematics where words are replaced by symbols and where the operations of connecting the symbols are rigorously defined. In this way, scientists can condense information into one equation, i.e. into one single line of symbols, for which they would need several pages of ordinary writing.

―Fritjof Capra, The Tao of Physics