Fibonacci Sequence

The Fibonacci Series is 0,1,1,2,3,5,8,13,21,34,55,......

This Series is generated by adding two number before it :

for example :
5 is found by adding two numbers before it that is 2+3.

Similarly 8 is found by adding two numbers before it that is 5+3.

and so on..

The Fibonacci Sequence can be written as a rule such as
 X_n=X_n-1 + X_n-2
For example : X_n-1=21 and X_n-2=13 Therefore X_n becomes 34.

When we  make a square as shown below we get a Spiral shape :

Golden ratio : If we take two successive number Fibonacci number we get a known as Golden Ration which has the approximate value as  1.61803399....
Bigger the pair of Fibonacci Numbers, the closer the approximation.

The symbol for Golden ration is φ (phi).


Fibonacci in Nature: 

The Fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner.
some of the images below shows the Fibonacci sequence in Nature


Fibonacci sequence in Cancer Cell Division

Fibonacci sequence in Galaxy

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(a+b)^2=a^2+2ab+b^2 But why?

So Lets prove it :
Consider a line 

Take any arbitrary point 

So now we can say that length of line is a+b
Now we have to square a+b
that will be

lets add all the squares and rectangles

This will be  a² 

Now it is a²+b²

Here there are two rectangle in the above diagram

As we know that Area of rectangle is Length X Width

So it will be a x b

Now lets add every square and rectangle

a² + b² + a x b + a x bi.e., a² + b² + 2ab

Thus 

(a+b)²=a² + 2ab+b² 

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Trick To Convert Fahrenheit and Celsius

Formula :-

To Convert Celsius to Fahrenheit 

°C  x  9/5 + 32 = °F  OR °F = (1.8 x °C) + 32

To Convert Fahrenheit to Celsius

 

(°F  -  32)  x  5/9 = °C OR °C = (°F - 32) / 1.8

Trick To Convert Celsius to Fahrenheit :

You will not get the accurate value of Fahrenheit using this trick.

Step 1 :  Double the celsius

Step 2 : Add 30

For example 

lets take 15 °C

Step 1 :  Double the celsius 15 x 2 = 30

Step 2 : Add 30 so 30 + 30 = 60°F

So it is quite near to the actual answer 59°F

Now to convert  Fahrenheit to Celsius 

Step 1 : Subtract  30

Step 2 : Divide by 2

Program To Convert Celsius to Fahrenheit and Fahrenheit to Celsius

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