Golden section

         Fibonacci Numbers and the Pascal Triangle

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Golden Section

The Golden Section and The human body

The Golden Section, also known as Phi, is manifested in the structure of the human body. If the length of the hand has the value of 1, for instance, then the combined length of hand + forearm has the approximate value of Phi. Similarly the proportion of upper arm to hand + forearm is in the same ratio of 1: Phi .


The human face abounds with examples of the Golden Section. The head forms a golden rectangle with the eyes at its midpoint.The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin.Phi defines the dimensions of the human profile. Even when viewed from the side, the human head illustrates the Golden Proportion.


The first golden section (blue) from the front of the head defines the position of the ear opening. The successive golden sections define the neck (yellow), the back of the eye (green) and the front of the eye and back of the nose and mouth (magenta).  The dimensions of the face from top to bottom also exhibit the Golden Proportion, in the positions of the eye brow (blue), nose (yellow) and mouth (green and magenta).

The human body is based on Phi and the number 5.The number 5 appendages to the torso, in the arms, leg and head. 5 appendages on each of these, in the fingers and toes and 5 openings on the face.The human body illustrates the Golden Section or Divine Proportion, also.The Divine Proportion in the Body :

The blue line, a golden section of the white line, defines the distance from the head to the finger tips

The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.

The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone.

The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline.

Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.


The DNA cross-section is based on Phi.A cross-sectional view from the top of the DNA double helix forms 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 : 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!


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.34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates Phi, 1.6180339.

There are many examples of the Golden Section or Divine Proportion in Nature. For example,the eye, fins and tail all fall at Golden Sections of the length of a dolphin's body. Phi is frequently expressed in many of Nature`s creations, and by varying the angle between adjacent radii, a number of Natural spirals and leafshapes can be created. The Fibonacci numbers form the best whole number approximations to the Golden number. Plants illustrate the Fibonacci series in the numbers and arrangements of petals, leaves, sections and seeds.Plants that are formed in spirals, such as pinecones, pineapples and sunflowers, illustrate Fibonacci numbers. Many plants produce new branches in quantities that are based on Fibonacci numbers.






  2001-2003 Radoslav Jovanovic              translated: D.Filipovic   created:  January 2003.