Fibonacci Series, Golden Proportions, and the Human Biology

Review Article

Austin J Surg. 2015;2(5): 1066.

Fibonacci Series, Golden Proportions, and the Human Biology

Dharam Persaud-Sharma* and James P O’Leary

Florida International University, Herbert Wertheim College of Medicine

*Corresponding author: Dharam Persaud-Sharma, Florida International University, Herbert Wertheim College of Medicine, Miami, FL, 33199, USA

Received: April 01, 2015; Accepted: June 25, 2015; Published: July 02, 2015


Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Keywords: Fibonacci; Surgery; Medicine; Anatomy; Golden proportions;Math; Biology


Classical geometry includes the traditional shapes of triangles, squares, and rectangles that have been well established by the brilliance of Pythagoras, Plato, and Euclid. These are fundamental shapes that have forged the great structures of ancient and modern day civilization. However, classical geometry fails to translate into complex non-linear forms that are observed in nature. To explain such non-linear shapes, the idea of fractal geometry is proposed which states that such fractal shapes/images possess self-similarity and can be of non-integer or non-whole number dimensions. Whereas classical geometric shapes are defined by equations and mostly whole number (integer) values, the shapes of fractal geometry can be created by iterations of independent functions. Observing the patterns created by repeating ‘fractal images’ closely emulate those observed in nature, thus questioning whether this truly is the mechanism of origination of life on the planet. Two important properties of fractals include self-similarity and non-integer or non-whole number values. The idea of ‘self-identity’ is that its basic pattern or fractal is the same at all dimensions and that its repetition can theoretically continue to infinity. Examples of such repeating patterns at microscopic and macroscopic scales can be seen in all aspects of nature from the florescence of a sunflower, the snow-capped peaks of the Himalayan Mountains, to the bones of the human body.

The observation of self-similarity belonging to fractal geometry found in multiple aspects of nature, leads to the question of whether such an occurrence is merely stochastic or whether it has a functional purpose. While a singular unifying equation to define the creation and design of life has yet to be determined, an un-coincidental phenomenon known as the Fibonacci sequence and the rule of ‘Golden Proportions’ may serve as a starting point for uncovering the methods of a universal architect, should one exist.

Fibonacci and rule of golden proportions

Fibonacci sequences: The Fibonacci sequence was first recognized by the Indian Mathematician, Pingala (300-200 B.C.E.) in his published book called the Chandasastra, in which he studied grammar and the combination of long and short sounding vowels [1,2]. This was originally known as matrameru, although it is now known as the Gopala-Hemachandra Number in the East, and the Fibonacci sequence in the West [1,2]. Leonardo Pisano developed the groundwork for what is now known as “Fibonacci sequences” to the Western world during his studies of the Hindu-Arab numerical system. He published the groundwork of Fibonacci sequences in his book called Liber Abaci (1202) in Italian, which translates into English as the “Book of Calculations”. However, it should be noted that the actual term “Fibonacci Sequences” was a tributary to Leonardo Pisano, by French Mathematician, Edouard Lucas in 1877 [3]. The Fibonacci sequence itself is simple to follow. It proposes that for the integer sequence starting with 0 or 1, the sequential number is the sum of the two preceding numbers as in Figure 1.