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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Degrees and Radians Calculator

Converting from Degrees to Radians

 Degrees can be converted to Radians with the help of this formula :

Radians = (Degrees x π) / 180

Converting from Radians to Degrees

Radians can be converted to Degrees with the help of this formula :

Degrees = (Radians x 180) /  π


Symbol : 1 Degree = 1°
               1 Radian = 1^c


1 Radian ≈  57.2958°

1 Degree ≈ 0.017460317^c

Program to calculate Degrees to Radians and Radians to Degrees

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Circumference of a Circle

Here is the formula to calculate circumference of a circle 

2 π r OR π d

Where r is the Radius of a Circle and d is the Diameter of a Circle... 

For example : Let the Radius of  a Circle be 5cm 

 So, Circumference of a circle = 2 x 3.141592 x 5

i.e.,  31.41592 cm

Here is a Program to Calculate Circumference of a Circle...

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Perimeter of a Triangle

Here is the formula to find the Perimeter of a Triangle....

Perimeter of a Triangle = a + b + c

where a, b and c are the side lengths of the triangle.

For example : Suppose the length of the sides are 5cm, 6cm and 10cm

Perimeter of the Triangle = 5 + 6 + 10

i.e., 21 cm

Here is the Program to Calculate the Perimeter of a Triangle..

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Perimeter of a Rectangle

Here is the formula to find the Perimeter of a Rectangle...

  

Perimeter of a Rectangle = 2a + 2b

where a and b are the breadth and height respectively...

For example : Suppose the breadth of a rectangle is 5 cm.

and height of a rectangle is 6cm.

so the Perimeter of a Rectangle = 2x5 + 2x6

i.e.,  22cm.

Here is the program to calculate the Perimeter of a Rectangle...

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Perimeter of a square

Here is the formula to find the Perimeter of a Square...

Perimeter of a Square = 4 x (Length of a Side)

For example : Suppose the length of a side is 5 cm.

so the perimeter of a square = 4 x 5.

i.e., 20 cm.

Here is the program to calculate the Perimeter of a Square..

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Calculate Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse

Here are some formulas to calculate Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse...

Note :-  a =  Side of a square.
             b =  Breadth.
             h =  Height.
             r =  Radius

Formulas

Square = a 2
Parallelogram = b*h
Trapezoid = 1/2* (b1 + b2)*h
Circle = π r 2
Ellipse = π r1 r2

Click on the Buttons to find Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse.


1) Click on the button to find the


2) Click on the button to find the


3) Click on the button to find the



4) Click on the button to find the



5) Click on the button to find the







Note : I have considered the value of π upto 3.14159265 in the above programs.

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