Consider the following sequence of numbers, where each term (apart from the first and second) is calculated by adding the preceding two terms;
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987….
To explain the sequence a little more, the 3rd term is calculated by adding the 1st and 2nd terms (1+1=2). The 4th term is calculated by adding the 2nd and the 3rd terms (1+2=3). The 5th term is calculated by adding the 3rd and 4th terms (2+3=5) and so on.
This arrangement of numbers is called the Fibonacci sequence. It was devised by an Italian mathematician Leonardo Bonacci around the late 12th century and oddly enough appears in numerous places throughout the world we live in.
If we were to take a look at a simple sunflower and see how many seeds are on it’s head we would find that they coincide with the Fibonacci series, i.e. 1,2,3,5,8….
Also, on many plants, the number of petals is a Fibonacci number. For example, buttercups have 5 petals, corn marigolds have 13 petals and daisies can be found to have 34, 55 or even 89 petals.
Just a simple coincidence? Guess again!
If we perform a simple mathematical operation on the series, we begin to see even more of these anomalies.
Take two adjacent numbers in the series and divide the smaller number into the larger one. As the numbers in the series gets larger, the division of these two numbers tend towards a single value - 1.6180339.
The division of any two numbers can be written as a ratio and that is what we intend to do here. For example, 13 divided by 8 can be written as 13:8 in ratio form. If we were to use large Fibonacci numbers say 987 and 610, then the ratio is 987:610 or roughly 1.618:1. This is what we call the divine ratio.
Often referred to as the golden ratio or the golden mean, it appears in an amazing number of places.
Firstly, a rectangle with the exact dimensions of 1.618 by 1 is known as a golden rectangle. After investigation, scientists have found that this is the most aesthetically pleasing rectangular shape.
If we were to draw a rectangle around our heads with the eyes at the midpoint, the rectangle would be in the dimensions of 1.618:1, a divine ratio. Not only this, but the mouth and nose are each placed at a distance from the eyes and bottom of the chin that also adheres to this divine ratio.
If you are still in doubt, investigate the dimensions of the DNA double helix. It measures 34 angstrom long by 21 angstrom wide for each full cycle of its double helix spiral. Both 34 and 21 are Fibonacci numbers and when divided give a rough approximation of the divine ratio.
The ancient Egyptians also used this ratio. It can be seen in much of their artwork, their hieroglyphics and some of their statues. Even the pyramids are built according to this ratio, with the ratio between the central height distance and the distance from this central height to the slanted edge being 1:1.618
Even the position of the three oldest Giza pyramids lie on what is termed a Fibonacci spiral, again because its dimensions are related to the Fibonacci sequence and the divine ratio.
It is worth mentioning here that the shape of the human ear and the swirl of a snail’s shell are also in the shape of Fibonacci spirals.
In 1509 Luca Pacioli published a book called the Divina Proportione, which explored the use of the divine ratio in architectural design. This was a major influence on subsequent generatios of artists and architects.
Le Corbusier, the famous architect also used the divine ratio as the basis of his Modular system of architecture. There are many other examples of the appearance of the divine ratio, like the arrangements of leaves, Fibonacci spirals on pinecones, ancient architecture being built according to the divine ratio.
So, with the divine ratio in use amongst the Egyptians, and as it turns out the Greeks also, it is clear that Fibonacci was not the one who first discovered the divine ratio. It seems like he only re-discovered it.
With a plethora of appearance in different forms throughout nature, the following question arises; is the divine ratio just some sort of coincidence or is it a divine clue left to humans know to make them aware that they are part of a much greater heavenly mechanism?
I’ll let you decide.
Feeds