The hidden symmetry in the arrangement of the leaves

"....surely Allah takes account of all things." (Surat an-Nisa’,86)

When we look at the plants and the trees around us, we see that the branches are covered by many leaves. At the first sight, you may think that the branches and the leaves on the structure of the plant were arranged randomly and disorderly. In fact, the exit places of the branches and the leaves on all the plants, which angle they will twist, or bend and the arrangement of the leaves around their branches, are all designated by a fixed mathematical rule.

When we examine this mathematical order in the plants closely, we encounter an impressive geometrical plan that amazes humans.

Plants obey the same mathematical rules down to the letter from the first day they were created. No leaf or flower stems by chance. How many branches will be on a tree, where will these branches stem from, how many leaves will be on a branch, and with what arrangement these leaves will be placed in are all predetermined. Besides, every plant has their unique rules for branching and leaf arrangement.

Scientist can define and classify the plants only by looking to these arrangements.

The extraordinary thing here is, for example, a poplar tree in China and a poplar tree in England are both seemingly aware of the same measures, the same rules and the same ratios. The one who created every plant with unique mathematical calculations in a most aesthetic manner, and the one who owns these aesthetic systems consisted from perfect calculations, is Allah, the Master of infinite wisdom. This is stated in a verse of the Qur’an like this:


He to whom the kingdom of the heavens and the earth belongs. He does not have a son and He has no partner in the Kingdom. He created everything and determined it most exactly. (Surat al-Furqan, 2)

The mathematical harmony of the leaves. Phyllotaxy

The arrangement of the leaves on plants was exposed by scientists with their many details, and this subject became a special research department in the science of botany. The leaf arrangement system which shows differences in every plant type is examined in the science of botany under the name of “phyllotaxy”. According to scientific research, every plant and every tree has a uniqe leaf arrangement ratio. Wherever you go in the world, this leaf arrangement ratio of the plants and trees, which share the same type, do not change. According to these ratios, which are also called "leaf divergence" in botany, the arrangement of the leaves around the body or branch of the plant is determined by a certain numerical order.

How is the ratio calculated?

We can explain the ratio calculation in this following way. If we name the number of tours starting from one leaf, then turning around the body or branch until it encounters another leaf with the same alignment as letter A, the number of leaves we encounter between these tours will be letter B, so the ratio named "leaf divergence" will be B/A.

In all the trees and plant types, the leaves are arranged according to this ratio without any change. The "leaf divergence" ratio, which forms a spiral with equal angles and differs according to every plant type, have numerators and denominators consisting of Fibonacci numbers which give us the golden ratio every time.

Leaf divergence ratios of some trees can be sorted like this:

In trees like elm and lime 1/2

In trees like beech, hazel and bramble 1/3

In fruit trees like oak, cherry and apple 2/5

In trees like rose, poplar, willow, pear 3/8

In almond tree 5/13

Without a doubt, there is an impressive geometric plan and mathematical calculation here. Wherever you go in the world, the ratio of the trees that we gave as an example above, will never change.

The Importance of symmetry on the leaves

Since the leaves are arranged according to the Fibonacci numbers, no leaf casts its shadow on the other. All the leaves can make use of sunlight and air equally.

Every leaf can catch water in the same amount, and because of that, the water which comes from the leaves flows down through the body and reaches the root of the plant.

In consequence, the root of the plant can take advantage of the rain water with maximum ratio in rainy weather due to the special arrangement of the leaves. Leonardo da Vinci, who was one of the famous painters and scientists of his era, explored this special arrangement of the plant leaves and explained its "advantages" like this:

" Leaf, always turns its upper part to the sky. Because of this reason it can absorb the dew in the air better, by using all its surface. Leaves arranged on the plant so that a leaf only cover another leaf with the lowest ratio possible. This arrangement of the leaves provides the necessary space for air and the sun to enter the plant. As a result of this arrangement a drop which falls from the first leaf to the fourth leaf can also fall down to the sixth leaf in the same manner."

The Golden Ratio in the leaves is under control of the Almighty Allah

It is clear that if every plant type on earth did not possess a unique leaf arrangement ratio, if the leaves of all the plants were scattered randomly and sloppy, the plants cannot make use of the sunlight, air, and rain water necessary for their needs. Depending on that, the plants balance of growth will break down and getting nutritions will be harder.

All these truths shows that the arrangement of the leaves on the branches are according to Fibonacci numbers and the vital functions that this ratio brings to the plants can only be explained by a perfect creation. Allah, who created everything completely with all their deepest details, bound the functions of the leaves to their places on the branch using this golden ratio. In a verse of the Qur’an, it is stated that everything takes place within the knowledge of Allah and is under His control:


" The keys of the Unseen are in His possession. No one knows them but Him. He knows everything in the land and sea. No leaf falls without His knowing it. There is no seed in the darkness of the earth, and nothing moist or dry which is not in a Clear Book." (Surat al-An’am, 59)

What is the Fibonacci Series?

Fibonacci series, which is a special series of numbers, took this name because it was first discovered by a famous Italian Mathematician Fibonacci who lived in thirteenth century. This series starts with the numbers 0 and 1 and continues to do so that every number in the series is the sum of the two numbers coming before itself. (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...) When the ratio of the numbers which constitute in the series with each other, we always get the numerical value of the golden ratio (1,618). This number series is the mathematical code of all the creation in nature which many scientists also accepting today. In the many geometric shapes in nature, the consecutive terms of this number series can be encountered.

It is a great miracle that all the trees which belong to the same type know about the golden ratio and follow the ratio predetermined for them. For example, how can a banana tree know about this ratio and follow it?

Accordingly, if you start from one leaf of the banana tree and make 8 tours, you will encounter the other leaf with the same alignment. You will also encounter 3 leaves between these tours. This ratio will never depart from this rule wherever you go in the world, from South Africa to Latin America. Even the presence of a leaf arrangement like this is one of the important proofs that living beings did not come into existence accidentally but were created with a perfect and complex ratio, calculation, and system. The one who encodes a ratio like this into the plants genetic structure and created them with special knowledge and ability is Allah, the Owner of superior wisdom and intelligence.


2011-04-23 17:37:36

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