What seems to be randomly selected parts of our world as we know it actually shares a deep connection with our life as we know it – the Fibonacci sequence. A sequence of numbers first described in Indian mathematics in 200 before Christ describes each part of the sequence as being the sum of the two preceding elements – starting with two ones. Leonardo of Pisa, known as Fibonacci and the name giver of the famous sequence, introduced the numbers that share his name to Western European mathematics.
The Fibonacci sequence appears in many aspects of our world, but also plays a significant role in various sciences, mostly being part of mathematics and computer science, but is also a considerable aspect of biology.
In math, you might find the sequence to be defined in terms of ‘recurrence relation’ as F0 equals zero, F1 equals one and Fn equals F n minus one plus Fn minus 2 for n being smaller than 1.
Many may find its significance boring or never stumble upon it because math isn't their field of interest. But the role the Fibonacci sequence plays in fields like nature is not to be underestimated - You can observe the branches of a tree, leaves on a stem, or even flower petals or pinecones develop, mimicking the order of the sequence.
Outside of botany, it is also noted in animals, such as the family tree of a honeybee or the ideal population rate of rabbits (see the Fibonacci rabbit problem), financial market trading, and architecture.
Wikipedia writes “In optics, when a beam of light shines at an angle through two stacked transparent plates of different materials of different refractive indexes, it may reflect off three surfaces: the top, middle, and bottom surfaces of the two plates”
While Wikipedia isn't the most reliable source in terms of research, I must admit to finding this part of the article strangely poetic. The thought of a mathematic discovery being woven in all parts of human perception, in all parts of our universe, gives me an odd feeling of comfort – the Fibonacci sequence connects our world, sketches intertwined lines between all cultures, all parts of our world; between us and nature, us and the world. We are all connected – not just through the same sky we share, the same stars and planets and air – but through this unusual pattern in nature that appears everywhere our eyes can see.
For humans to discover this order is something I find extraordinary, like a gift given from the universe itself; helping us to not just see but understand the world around us, its ways and quirks and life.
Even our bodies display this peculiar connection. ScienceDirect writes “(The) Golden ratio or Fibonacci sequence occur in human body as in every manifestation of life. The superimposed human hand approximates to the golden spiral which resembles golden rectangle”.
Whether you believe in some variation of a divine force or not at all, something created us and the world to have this one thing, this undeniable order in common. It is a phenomenon that unites us – transcending culture, language, even form of life. It is just present, in all of us, connecting old and young, spiders and flies, artists and scientists – through all differences, all demographics; it is there, omnipresent and constant.
While some might find this disconcerting or straight-up perturbing, I find a sense of comfort in this knowledge science grants us. Not only does it make me feel like part of something grander, but it counteracts the feeling of loneliness – disconnection – that is part of our society.
We can identify symmetry in a time span not exceeding 0.05 seconds. It is somewhat of a natural ability that is shared by all eyesight-possessing people. It is a part of many famous and cherished art works of our time. Examples include Doryphoros by Polykleitos, dating back to around 440 before Christ, who included the ‘golden ratio’, somewhat one of the few rules in art, effortlessly. Another one is The School of Athens by Raphael, an oil painting we all know of today, who was directly referencing the golden ratio in his paintings. Many more of his now famous works were composed with this ratio – and therefore the Fibonacci sequence – in mind. Even the Mona Lisa somewhat falls in this category of the fusion between art and mathematics.
The Fibonacci sequence is credited as an “aesthetically pleasing principle”, being present in nature, human bodies and space, and achieves a more flowing artwork – a natural instinct, given its presence in our midst.
The often referenced ‘rule of thirds’, deriving from the Fibonacci-inspired golden or divine ratio, balances the features of an artwork – whether it is photography or a painting – and makes it more visually appealing to the viewer.
First noticed in art from the Renaissance onwards, it remains a shaping component in many art works that we admire today. Mark Mitchell – Paintings and Drawings describes the effect and uniqueness of it like this: “The most interesting aspect of the Fibonacci spiral is, perhaps, the fact that it can be forced or simply found. Last year, it was even observed in a journalist’s photograph of brawling Ukranian parliamentarians”, suggesting to me that if you look hard enough in the proper places, you will be met with the sequence of life in the most remarkable and unexpected forms.
Moving away from the Wests’ fascination with the Fibonacci spiral’s significance, we can observe and recognize it even in ancient Egyptian art and architecture, as a blog on the website egyptmythology claims, evident by its introduction “Uncovering the ways in which this mathematical concept influenced the design and aesthetics of one of history’s most remarkable civilizations”.
In Egyptian culture, specifically in art and architecture, high value was placed on symmetry and proportion, creating harmony and aesthetically pleasing works. Including mathematical concepts, a term under which our focus point, the Fibonacci sequence, falls as well, into their designs was a process of mixing practicality and their spiritual beliefs.
It is known that the Egyptians thought of mathematics and geometry to be God-given gifts, opening the possibility of them creating structures of functionality and intertwine them with ‘meaning and significance’, based on their belief systems. In addition to that, they embraced the concept of the connection between nature and mathematics, two God-given elements. In art, the incorporation of math in the depiction of nature enhanced beauty and meaning.
Furthermore, the Fibonacci sequence links to the philosophical understanding of the universe that was widely spread through Egyptians, characterized by the interconnectedness of all things. Factoring into that, there’s also an alleged link between spirituality and the ‘language of divine’- mathematics. The use of it in artworks and architectural creations represented a deeper connection to the universe and nature. Or so the blog, diving into this topic, claims. However, the author is not providing any proof or context with this, so it shall only be treated as a hypothesis.
If one is thinking of Egyptian architecture, the first thing coming to mind are most likely the Great Pyramids of Giza. Those iconic structures implement the Golden Ratio, deriving from the Fibonacci spiral. In the case of the Pyramid of Khufu, the largest of the trio in Giza, its measurements show a close relation to the Golden ratio. Its base measures 230.4 meters, while its height is 146.6 meters. The two numbers are close approximates of the Golden ratio, linking its architecture and the mathematical Fibonacci sequence.
Another instance of the Fibonacci sequence shaping and influencing architectural choices in Egyptian history is the alignment of the pyramids. Their cardinal points and implemented geometric shapes show deep understanding of mathematics and are likely linked to the Fibonacci sequence.
A few other examples of its significance include historic Egyptian temples and monuments, further underlining the role the Golden ratio played in the architecture of old Egypt. But its influence can also be discovered in Egyptian art, which is known ‘for its adherence to strict conventions’. This includes paintings, reliefs and sculptures which inhabit a strong balance and harmony. Even in nature-based elements, there are patterns and composition showing spirals or growing natural elements that incorporate the characteristics of the Fibonacci sequence.
The relevance is still to be spotted today, extending into modern and contemporary Egyptian art. Artists study ancient mathematical concepts to draw inspiration for an artistic expression of the past and the present in their art.
The sequence is continuously used by artists and architect to create works of harmony and meaning, showing its omnipresence in all aspects of our lives – aspects we’re often too busy to notice, ones that disappear from us in a moment of rush or preoccupation; and that is what makes it so beautiful