If you enjoy math, geometry, mystery and science, this subject might interest you. It is too complex for a simple blog post. Here are some highlights and I will include links if you find this subject as intriguing as I did. Enjoy.
Phi, also known as The Golden Ratio or Divine Proportion, Golden Section, Golden Mean, is represented by the number 1.61803399. The digits can go on forever without repeating. We will simplify it to 1.618.
The Fibonacci Sequence is nature's numbering series and provides another way to derive Phi mathematically. The sequence of numbers is quite simple. Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The approximate ratio of each successive pair of numbers in the sequence is 1.618 or Phi. (Example: 5 divided by 3 = 1.666.) As you go further into the sequence and more digits are added, the ratio gets closer to the exact figure of Phi.
Both The Fibonacci Sequence and Phi represent the same number, 1.618, therefore they are inseparable. When Phi is mentioned, know that The Fibonacci Sequence is also there.
Why were the early Greek and Renaissance artists, scientists, architects, musicians and astronomers so fascinated by this number? Why did Dan Brown use Phi as a plot element in his novel, The Da Vinci Code? Why do we still use Phi today?
“Phi creates a sense of balance, harmony and beauty in the designs we find throughout our natural world and the universe thereby creating a sense of harmonic relationships and spiritual connections.” Since ancient times, man has applied both Phi and The Fibonacci Sequence consciously and unconsciously to achieve balance, harmony and beauty in art, music, architecture, design and religion.
The influence of Phi may be seen in the works of the early artists such as Da Vinci, Raphael, Botticelli and Seurat, right up to present day artists. Musical scales and compositions and the dimensions of musical instruments, such as the violin, all show the influence of Phi. Architecture, such as the Notre Dame in Paris and the Greek and Roman Temples are another example. Industry uses Phi in the design of their logos and products, such as cars and fashion. In medicine, Phi is used as a guide in both facial plastic surgery and cosmetic dentistry.
The Fibonacci Sequence and the influence of Phi appear everywhere. In nature they are is seen in the leaf and petal arrangement in plants and flowers, the bracts of a pinecone, the scales of a pineapple, the arrangement of seeds in a sunflower. Many insects and animal dimensions are based on Phi, such as the spirals of seashells, the body sections of ants and other insects, wing dimensions, etc. Even in the arrangement of the bones of our hands and the spirals of human DNA. Astronomers have found Phi and the Golden Ratio relationships in our solar system and the universe.
We didn’t invent Phi or The Fibonacci Sequence. It was always there. It is as old as the universe. Some Theologians believe that Phi is linked to the Creation.
Pretty interesting reading.
Two related topics that you might find interesting:
The Golden Rectangle – the most pleasing rectangle with sides having a ratio of 1.618. (Phi again).
Rebatment – the two squares within a rectangle and its importance in composition and the formation of the Fibonacci Spiral.
And the links:
Thanks for visiting.