The Golden Spiral Unveiled: The Beauty of The Fibonacci Sequence

Do the geometrical patterns of a flower, snowflake, and seashell happen by a chance? How about the possibility of producing productive pairs of rabbits? Why there are a precise number of seeds in a sunflower fill the space effectively without leaving any gap? And why you can't even find a four or more leaved clover? Is everything happening by a coincidence? This Fibonacci sequence essay clearly explores the mathematical marvel and artistic applications of this fascinating numerical pattern.

All these things above are connected by a common theme of nature. These are said to have patterns, series, and sequence which is known as Fibonacci was invented by the Italian Leonardo Pisano Bigollo in 1202. We don't just see Fibonacci Sequence where the series is got by adding 0 and 1, followed by the result and the previous number but his sequence has intricacies and subtleties. Fibonacci Sequence is so closely related to Golden Ratio and has a tremendous impact on many aspects of nature, on human and animal body proportions, architecture, paintings and in many areas as well. This seems magic of Fibonacci I've realized yet ubiquitous interconnectivity between living beings and the universe is vastly astounding and fascinating.

All the examples mentioned above express the Fibonacci Sequence. The spiral patterns of the shell, the array of seed of a sunflower or the total number of its petals, the growth points where some of the branches form or split, even our DNA molecules and many more phenomenal patterns are all reflects the Fibonacci sequence and this also has a connection to Euler's formula developed by Leonard Euler, present in both X and Y formulae that its resemblance is not a mere coincidence. We don't need to go too far for the evidence, just by looking ourselves in the mirror we will notice that most of our body parts follow the numbers in Fibonacci Sequence. Yet our human body are in symmetrical form in terms of Golden Ratio. This was clearly shown in the Vitruvian Man of Da Vinci. 

I was mesmerized by how these things followed a pattern and related to The Divine Proportion which in the book of Luca Pacioli emphasized its application of golden ratio in architecture and art thus it is evident to some of the artworks of Da Vinci. One of his painting is the Last Supper yet considered as the best illustration of its use of divine proportion where there is an alignment between the architectural designs and even the position of the disciples are believe to be in proportion or has the evident of Golden Rectangle also the famous Mona Lisa are said to have Golden Ratio and Golden Spiral. 

However, through careful analysis, some of the paintings of Da Vinci are not all show the evidence of the Golden Ratio. 'The Misconceptions of the Golden Ratio' by Dr. Markowsky provides deeper analyzation and accurate information about this misconception of golden ratio. He then, sited that 'the measurements of real objects can only be approximations'.

To sum up, some people say, this Fibonacci Sequence is found anywhere on Earth and also a proof that there is a supernatural power or creator existed where these creations are believed to be a phenomenon. God created everything on Earth symmetrical. These are not only design but intelligent design.