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Today, you are going to see something very interesting........

Okay, let’s begin

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a

b

Our finger is split into three parts. Let’s measure the length of the finger.

Now, let’s measure the length of these two parts.

a/b = 1.618

Let’s divide both of these.

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Now, let’s measure the length from the tip of the middle finger to the wrist.

Let’s measure the length from the wrist to the elbow.

On division, we get the same number again!!!

a

b

a/b = 1.618

WEIRD????

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Now, let’s try one last thing....

a

b

Let’s divide the entire length of the arm

to the length from the tip of the finger to the elbow.

a/b = 1.618

AMAZING!!!

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This person is a model. Let’s divide the length of her face

to the width of her face.

a

b

a/b = 1.618

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Now, let’s divide the length of her mouth

to the width of her nose.

a/b = 1.618

a

b

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What is this?

1.618

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It is commonly known as:-

DIVINE RATIO GOLDEN RATIO FIBONACCI RATIO phi ( Φ )

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This ratio can be found in:-

Animals Plants Humans Good Architecture Maths Art And everywhere....

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I literally mean everywhere because this golden ratio or divine ratio has been popping up all over the place dating back as far as 3000 B.C.

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And nobody knows who figured this out first.

Europeans

Indians

Egyptians

All that people knew was that this weird number was all around them.

1.618

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This number can be found in designs of honeycombs to your own body which you just saw.

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Then, in the year 1202, there was a guy, Leonardo Pisano, better known as Leonardo Fibonacci.

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He had to tackle a bunny rabbit problem. WHAT’S BUNNY RABBIT PROBLEM?

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. How many pairs will there be in one year ?

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The solu­tion, gener­a­tion by gener­a­tion, was a sequence of numbers later known as Fibonacci numbers.

1,1,2,3,5,8,13,21,34,55,89.....and so on

The next number is the sum of the two previous numbers in the sequence.

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FIBONACCI SERIES

Let me show you something. Let’s divide each number by the immediate previous number and see what we get. Let’s begin with 2.

1,2,3,5,8,13,21,34,55

2/1 = 2 3/2 = 1.5 5/3 = 1.67 8/5 = 1.6 13/8 =1.625 21/13 = 1.615 34/21 = 1.619 55/34 = 1.618

And, if you continue this process, you will notice that at this point the number becomes really close to 1.618 but does not reduce any further after that.

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Now, you have seen the wonders of 1.618 .

If you take a pineapple, a pine cone or a sunflower

and count the number of spirals

it will always be a Fibonacci number

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Now, look at this.....

1X1

1X1

2X2

3X3

8X8

5X5

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This is a Fibonacci spiral.

Does it look familiar? May be like our ears.....

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Check out this image of the big waves and guess which figure does it perfectly fit into?

Yes, a Fibonacci spiral!

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And what else do you see with such spirals?

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Let's go completely microscopic.

This is the DNA of our cell which has a helical structure.

The ratio between the maximam length to the maximam width between the two spirals is....

Yes, it is 1.618.

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Let's go completely large scale.

The spiral formed by the galaxies is Fibonacci spiral.

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1.618 is known as the divine ratio because people believed that the almighty has incorporated this number into all his designs over the universe as you just saw; but, of course we can never know it for sure.

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Thanks for your kind attention

VRINDA NARULA CLASS - 10