The Perfect Spiral

Shivani Pujari, Dedicated Writer

The world is a mysterious place. Some people think everything happens for a reason. Others believe that there are no true explanations for anything and everything that happens. There are a multitude of unknowns in the world; it’s easier to say what we don’t know than what we do. Two of these mysteries have names: the Fibonacci sequence and the golden ratio.

The Fibonacci sequence and golden ratio (two slightly different ideas) make objects appear pleasing to the eye. This is because of the dimensions of the parts—for instance, spirals of succulent leaves (image to the right)—where the ratio exists, are proportional. Proportional objects are appealing to the human eye as they are aesthetically pleasing.

The ratio can be obvious especially in the form of a spiral, like in a nautilus shell (below left) or a logarithmic spiral (above left), but can be more subtle in others, and must be examined more closely to be perceived, like in the whorls of sunflower seeds or florets (below right).

The Fibonacci sequence mathematically creates an approximate ratio of 1.6 (the golden ratio). Two consecutive numbers in the sequence can be divided (the larger value by the smaller value) and a number close to the golden ratio will appear. As the numbers you choose to divide increase, the quotient moves closer and closer to the real irrational golden ratio. The Fibonacci sequence itself is reached by first adding 1 and 1, then adding the previous sum to the most recent sum. For instance, starting at 1 the sequence would be: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, or, 1, 1, 2, 3, 5, 8, 13, and so on.

Examples of the sequence most often occur in nature, as mentioned above. There are various other intriguing places in which the number is evident, though. The sequence is used in interior design and photography as it helps the designs and photos look attractive.

Nature is not always consistent. Each and every flower or blade of grass is different, regardless of how similar they look. So, this begs the question: How can something as consistent as a number appear in something as inconsistent as nature (including humans)?

Scientists and ordinary people alike have often wondered whether or not the golden ratio is present in the human body. There are varying degrees of disagreement within the subject. Some experts say yes, numerous individuals have a face that is congruent to the golden ratio which makes them look ‘beautiful’, while others disagree.

According to, in 1855, German psychologist Adolf Zeising wrote and published a book on the golden ratio, which included many insights on the topic, including the fact that the distance between the navel and toes divided by your total height gives you the proportion, roughly rounded to 1.6. However, this is not true for the majority of people, so the controversy persists.

The fallacies and gospels surrounding the golden ratio are the most interesting part of the subject. For instance, as mentioned before, whether or not the golden ratio appears in humans is still widely debated. There’s also the matter of whether or not the Fibonacci sequence actually can occur in anything outside of mathematics. “Live Science” states that some people, when looking for the golden ratio, simply look for a ratio that equals 1.6. However, the real ratio consists of two segments of something whose ratio is proportional to that of the full segment to the complete object. For example, if a piece of string was cut into two unequal pieces, and the ratio of the two pieces was proportional to the ratio of the entire piece to the entire ball of string, the golden ratio would be present. The image on the right is a visual representation of what was explained above. The A and B are a ratio that is proportional to A+B, or the whole.

The Perfect Spiral


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People know that the Fibonacci sequence and golden ratio exist but they don’t know why they exist. Why would something be in shells, flowers, and photography? The ‘I don’t knows’ about the two subjects are what make people so interested in them. What do you think? Is there a reason behind the Fibonacci sequence and the golden ratio, or are they simply inexplicable?




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