Phi: A value which specify beauty

“Even nature is incomplete without mathematics, than who are we to snub it.”

Do you think you are beautiful? Think again because beauty has it’s own ratio.

Yes, a ratio define everything that looks beautiful.

I have mentioned phi in my title. Let’s have a look on phi.

Phi=1.61803398875………..

An Italian mathematician Luca Pacioli wrote a book named “De Divina Proportione ” in 1509.

The mathematician Pacioli studied drawings of Leonardo da Vinci that initiated the value of phi.

A ratio that defines beauty is 1.618:1.

Everyone knows about a famous painting “Girl with a pearl earring” painted by Johannes Vermeer. This is one of the most beautiful painting in world.

Girl with a pearl earring

The dimensions of this portrait is (17.5in*15in) and the ratio between these dimensions is 1.6:1 which is approximately equal to 1.618:1.

If you have studied Fibonacci sequence(0,1,1,2,3,5,8,13………) you must know how Fibonacci sequence and phi are interconnected to each other.

The proportion of numbers of Fibonacci sequence converges to a value and that value is 1.618 or its inverse 0.618.

The ratio 1.618:1 is also known as golden ratio.

Golden spiral

Golden spiral

If we will measure the proportion of length of these lines from the smallest one to the largest one it will be approximately equal to 1.618………

Snail shell

Snail shell

A snail shell follows the pattern of golden ratio.

Human ear

Human ear

A human ear also form a pattern of golden spiral.

Plants

Fiddlehead fern

These are Fiddlehead fern found in mountainous area, these also forms the pattern of golden spiral.

Everything in nature form golden spiral in any form from pyramids to a small invisible atom.

Ok! This was a small hint about phi. Hope this blog make you gain some more knowledge about mathematics and it’s relation with nature.

Now, go around, look for the beautiful things, find their ratio’s and understand more about phi and beauty of nature.

Also, have a look on yourself and measure your beauty with the help of phi.

“You will start loving the thing’s you hated the most, if they makes you more beautiful”

Beauty generated by mathematics in nature

“BEAUTY OF NATURE IS WRITTEN BY THE ALPHABETS OF MATHEMATICS”

Many times a question arises in our mind that “did nature also need mathematics to define itself?”

The answer is yes. Mathematics is present all around us in fact our body is also defined by mathematics.

Before I will start with what I want to convey, there is something you must have to know,

Mathematics is a way to understand the nature in its pure and actual form.

Have you heard about Fibonacci sequence?
I will tell you something about it and how it is linked to everything around us.

Fibonacci sequence:- Sequence of nature

It is sequence of numbers in which each number is the sum of preceding two numbers.
This sequence look like 0,1,1,2,3,5………….
Mathematical formula:- Xn+2=Xn+1+Xn.
The Fibonacci sequence was already presented in nature all around us but founded by an Italian mathematician named Leonardo Pisano Bigollo(1180-1250)Now, how this sequence is related to nature?
Have you ever observed geometry of plants, flowers, branches of tree etc?
Yes, of course nature have generated them but in the language of mathematics.
By the help of these few examples I will tell you how mathematics and nature are related to one another.

Flowers

Sunflower

This sunflower is forming the golden spiral and the seeds of sunflower are in the form of Fibonacci numbers.
We can also look at the petals of some flowers around us they are also in the form of fibonacci numbers like butterfly Mariposa have 3 petals, tulip have 5 petals, berlandiera lyrata have 8 petals, etc.

Trees

Tree diagram

This is a simple diagram of tree which properly show that the branches of tree are in the form of Fibonacci numbers.

Plants

Cactus plant

This is a cactus plant which also forms a golden spiral and has it petals in the form of Fibonacci numbers.

Human body

Skeleton of human hand

Look at this skeleton of a human hand from tip of index finger till wrist. The length of each bone seems like the sum of lengths of preceding two bones. And this is what Fibonacci sequence explain.

These were the few examples which proves that we are surrounded by mathematics or mathematics surround us all.

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Do you all now agree with the fact that mathematics is all around us?
Now you can explore around to look at the nature and find out many more such examples of nature which contains mathematics.

Ok! That was all that I want to convey…. hope you gained something new. This is my first blog next time this blog page will have more mathematics and much more beauty. I will eagerly waiting for your comments.

“We have everything around us, but we have to explore to make it with us.”