Animals

 According to theorists Boeyens and Thackeray, The Golden Ratio is reflected in birds and in animal kingdoms, from large scale to minor entities. 
For example, according to Boeyens and Thackeray, The Golden Spiral is visible even in elephant tusks, and as I was observing it, I realized that even its gathered trunk reflects the Golden Spiral. 




Moreover, the Golden Spiral is also reflected in the horns of a ram.


Matila C. Ghyka, a novelist and theorist identified a golden ratio between the leg of the horse and the vertical thickness of the body. 

According to Akhtaruzzuman and Shafie, even a penguin's body reflects the proportions of Golden Ratio; with the eyes, beak, wing, and significant markings falling at the top golden sections. 

The peacock's feathers are one of the most beautiful example of The Golden Ratio in nature. 

The Golden Ratio and Fibonacci Sequence in more distinctly minute features includes "microtubules" of animal cells. In mammals, each of these is comprised of 13 columns; 8 of which are lefthanded and 5 of which are righthanded, and these are all Fibonacci numbers. In case of double microtubules, the number of columns is 21, the next number in the sequence.  While Livio contradicts the possibility, many theorists insist a potential  causal/correlation between these numbers and more efficient information processors. Livio considers it potentially coincidental. 

Between 1810 and 1876, lived a German psychologist,, Adolf Zeising, and while observing animal skeletons and bones. The branching veins and nerves allowed him to establish a link to the Divine Proportion. 

Comments

Post a Comment

Popular posts from this blog

Art

Image
 The Golden Ratio And Fibonacci Sequence In Art And Architecture  Although humans are blessed with the gift of nature, we tend to enjoy aesthetically pleasing order and symmetry. According to evidence, humans are likely to detect symmetry in as little as 0.05 of a second! It is evident that humans do not only like seeing symmetry and Divine Proportion, but also working to create and display it. It can be seen in art and architecture.   In paintings, portraits and drawings, artists like following it.  Vitruvian Man (Leonardo Da Vinci)  The Great Wave (Katsushika Hokusai)   The Last Supper (Leonardo Da Vinci) Mona Lisa (Leonardo da Vinci) Rembrandt's Self Portrait Mondrian, Tableau 1. For example, the Vitruvian Man exhibits a pentagonal symmetry, and the square side to circle radius ratio is the golden ratio. The dimensions of the table and the proportions of the wall and background in Da Vinci's "The Last Supper" display an attempt of following the gold...
Read more

Topic: The Golden Ratio

 The Golden Ratio The golden ratio is described as a ratio between two numbers that equals approximately 1.618. It is also referred to as the golden number, golden proportion or the divine proportion.  The Greek letter  " φ" (phi) is used to denote the golden ratio.  It is often associated with the Fibonacci sequence, which is a naturally occurring series of numbers, in which each number is added to the last. Although the golden ratio is vastly viewed as a mathematical ratio, it can be found anywhere. In the creation of every balanced thing around us, r anging from nature and architecture , to paintings and music, it plays a part. It is often applied advertently to create an organic and aesthetically pleasing composition.  
Read more

Music

Image
  Mathematical harmony has, over the years, been used deliberately and unknowingly in musical composition. Mathematician Gottfried Leibnez wrote that "music is the pleasure the human mind experiences from counting without being aware that it is counting." Italian composer and lutenist, Vincenzo Galelie also wrote a discourse on string theory, which states that "the universe is constructed by tiny vibrating particles", which are assumed to be even smaller than subatomic particles, and these interact with each other by twisting, folding and vibrating. They create phenomena like electromagnetism and gravity. This string theory may also be linked to sound and hence music.   Composers often rely on the golden ratio and Fibonacci sequence to enhance their compositions, and construct balanced, melodic, dynamic movements and rhythms. Claude Debussy's music, for example, use the golden ratio, prominently the "dramatic" climax of "Cloches a travers les feui...
Read more