Fibonacci Series in Nature

---

Fibonacci Series is just a simple sequence just add the previous two numbers in the sequence you got the next one.

with F1=F2=1 and F0=0 .

The Fibonacci numbers for n=0,1, 2, ... are 0,1, 1, 2, 3, 5, 8, 13, 21, ... ∞.

Don't worry I'am not going to tell that big complex equation related to Fibonacci Series, that was just
for a quick review, here I want to show you the beauty of this equation, to show that the numbers that occur in this series are Nature's number.They appear in nature so frequent that you will be amazed, they appear from flower petals, the bracts of a pine-cone, or the scales of the pineapple, to the shapes of Galaxies.In this random Nature you will you will find many instances where this series applies.


Probably most us never give time to examine our surrounding if you were then you should find that the no. of petals on a flower is one of the Fibonacci numbers.One petal flower like white calla lily, two-petaled flower is not that common but it there like euphorbia, three petals in trillium,....,13 in black-eyed susan, 21 petals in shasta daisy.







But how this happens plants, don't know this sequence , they don't use symbols like us, they just grow in most efficient way.Same you can see the leaf arrangement, or phyllotaxis(study of the ordered position of leaves on a stem), one reason may be with the help of this arrangement the light falling on each one maximizes, which is important for the growth of plants.



The leaves on this plant are staggered in a spiral pattern for optimum exposure to sunlight.By apply the Golden ratio (it is an irrational number whose value is 1.61803....) to a circle we can see how this plant exhibits Fibonacci qualities.Next time you go into your garden just look for it.



By dividing circle in such a way that the ratio of the arc length equals to Golden ratio, we find the angle of the arcs to be 137.5 degree , this is the same angle at which adjacent leaves are positioned around the steam.This phenomenon is observed in many types of plants.

In the case of pine-cones or pineapples, we can see a double set of spirals one going in clockwise direction and another in anticlockwise direction.When these spirals are counted, two sets of Fibonacci numbers are found.


Similarly, sunflowers also use this technique to grow of seed on their seed head, Golden Spiral seed arrangement allows them to maximize the numbers of seeds that can be packed into a seed head.


Why?

Any number that is fraction ex; 0.5 is 1/2 or .25 is 1/4 will, after a while make a pattern of line stacking up which will create gaps. But the Golden Ratio(represented by a Geek Letter φ-phi) is not a fraction, it is an irrational number that's why the gaping doesn't happens.
When we divide all adjacent  Fibonacci numbers their ratio is very close to Golden ratio.

Many fruits also show Fibonacci relation to nature like inside the banana there are three section or in apple there are 5 section .



Fibonacci Numbers are not just limited to Plants it also appear in Animals too.The shell of the Snail shell and chambered Nautilus has Golden Spiral (Spiral made by the square having side length of fibonacci numbers) and it is called logrithmic spiral. This spiral can be repeated infintie times, which seems to bound the nature. Horns of some goats also seem in this shape, and the shape of certain spider's web.



Have you observed some people got easily attraction while other's not, some have great eyes, "beautiful" smiles, "attractive" physic, the secret behind it is Golden Ratio. It is seen that the people whose body dimension very close to golden ratio got more attraction. Both Human and Non-Human body have many examples of Golden ratio. The mouth and nose are positioned in the golden section of the distance between the eyes and the chin.Similar proportions can be seen in our arms,leg and head.We have 5 fingers in each of the hands, same number with foot fingers, 5 openings of the face, 5 major sense of organs for sight,sound, touch , taste and smell and many more [5 is the 5th Fibonacci number].






Look carefully the above picture of a Galaxy have find something common ? Yes, this is the same logarithmic spiral that we have seen in the Snail shell, they also follow the familiar Fibonacci pattern.Our Milky way galaxy has several spiral arms, each at about 12 degree .

Here I have listed few of the amazing phenomena that follow Fibonacci Pattern.You will find even more, like DNA, cells which are fundamental part of life, but nature doesn't follow this rule everywhere, he have more methods of living.So, observe your surrounding and you will find more examples and let us know in the comments.