The universe in a spiral

Gazing at the world around us often leaves us astonished with its beauty, but how often do we move our gaze beyond what is not visible to everyone’s eyes? Have you ever wondered what your face has in common with an egg or how is a chameleon related to a pineapple? The universe is a magnificent and complex place where the relationship between seemingly unrelated things can be found. The innumerable repetitions of patterns in nature that give rise to these mesmerizing scenarios can be easily explained mathematically.

The pineapple follows the Fibonacci sequence. Source: Pixabay

Leonardo Pisano, son of a Pisan merchant and a mathematician, introduced a series of numbers that later became a subject of interest, debate and research for the next hundreds of years. The series and its derivatives have been found to be useful in deriving and explaining innumerable phenomenon ranging from modern-day finance, computation and programming to art and natural phenomenon, and is now famously known as The Fibonacci Series.

Fibonacci as starting point of life. Source:

Its a series of numbers, and what else?

Fibonacci series is a sequence starting from zero in which the sum of (N-1)th term and (N-2)th term gives the Nth term i.e. the sum of the preceding two terms. In simpler terms, the series is as follows- 0,1,1,2,3,5,8,13,21,34,55,…. This series was found to be applicable in a number of natural phenomenon such as the number of petals on certain flowers-  lily with 3 petals, buttercups with 5 petals, chicory with 21 and daisy with 34 petals, in the splitting of tree branches in certain trees like a sneezewort, where the main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stem branches into two, while the other one remains dormant.

Chameleon’s tail in a Fibonacci Spiral. Source: MNN

Looking around!

The Golden Ratio is of the derivatives of the series, denoted by the Greek alphabet Φ (phi). Φ is the ratio of the Nth and (N-1)th term of the series and is a constant 1.618. The length and breadth of the DNA, the number of female honey bees to the number of males honey bees in a colony, faces, both human and non-human, with the mouth and the noses positioned at golden sections of the distance between the eyes and the bottom of the chin, all exhibit the proportions of the golden ratio.


Another derivative, widely found around us is the Golden Spiral and the golden rectangle thus formed. A Fibonacci or Golden spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The head of a flower, most commonly seen in the heads of sunflower, seeds are produced at the centre and then migrate outside to fill all the space in spiralling patterns. More examples may be found in the arrangement of seed pods on a pine, cauliflowers, pineapples, with each unit consisting of a pair of spirals, each one spiralling upwards in opposing directions with the number of steps almost always matching consecutive Fibonacci numbers. Snail shells, cochlea of the inner ear, horns of certain goats, the shape of certain spiders’ webs to macro phenomena such as the shape of cyclones and spiral galaxies such as our own Milky Way galaxy abide by this golden ratio.

Fibonacci Spiral Galaxy. Source: briankoberlein

Owing to its application in a plethora of micro as well as macro phenomena, the existence of golden ratio that was once just found in nature is now easily found in man-made objects as well. What was once confined merely to the Renaissance paintings is now observed in architecture, computer programming, even finance and a huge number of our day to day objects. Thus, we must look around and open our eyes to the ceaseless wonders that owe their existence to this golden series of numbers.


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