posted 9/5/2010 by Vijendra Shakya

**What is Fibonacci
series?**

Sequence is set of objects (numbers) which are in Orders.
Fibonacci series is a sequence of list of numbers which is invented by Leonardo
Fibonacci (fi-bo-na-chee) in 1202; on the name of Leonardo Fibonacci it is
named “Fibonacci series”.

Fibonacci series are:

0,1,1,2,3,5,8,13,21,34,55………

In Fibonacci series first two numbers are 0 and 1 after that each subsequent number is the sum of previous two numbers i.e.

f0=0, f1=1 now f2 will be sum of f0 and f1 and f3 will be sum of f1 and f2 like:

f2=f0+f1, f3=f2+f1

fn=fn-1+fn-2

Seed values of the f0=0 and f1=1.

Here I have tried to generate the Fibonacci series through the
C# code. We can do this as follows:

public void FibonacciSeries(int 10)This will return first 10 Fibonacci series term.

{

int f0 = 0;

int f1 = 1;

for (int i = 0; i < 10; i++)

{

//First assign the initial value to the fn.

int fn = f0;

//Print the fn value

Response.Write(fn + ", ");

//calculate fn for the next step

fn = f0 + f1;

//now f0 become f1 and f1 become fn

f0 = f1;

f1 = fn;

}

}

OUTPUT:

0,1,1,2,3,5,8,13,21,34

In a Fibonacci series a number is a Fibonacci
number if that number follows the following condition:

5fn^2 + 4 OR 5fn^2 - 4 is a perfect square, here fn is
the positive integer number. I.e. fn is a Fibonacci number IFF one of 5fn^2 + 4
OR 5fn^2 - 4** **is perfect
square.

A perfect square is a number that has a **whole
number** as its square root. (I.e. X^2 is equal to X times X)

To check the number (X) is perfect square or not first we calculate the square
root of the number (Y) after that we calculate the square of the square root value
(Y) if Square of Y is equal to the X then number(X) is a perfect square.

public void IsFibonacciNumber(int number)We can test this in C# as follows:

{

//by the rule first we calculate 5fn^2 + 4 and 5fn^2 - 4

double f1 = 5 * Math.Pow(number, 2) + 4;

double f2 = 5 * Math.Pow(number, 2) - 4;

/*now we check one of in f1 or f2 is perfect Square root or not*/

//find out the SquareRoot of the f1

var sqrtF1 = (long)Math.Sqrt(f1);

//find out the SquareRoot of the f2

var sqrtF2 = (long)Math.Sqrt(f2);

//find out the square of the sqrtF1

var squareF1 = Math.Pow(sqrtF1, 2);

//find out the square of the sqrtF2

var squareF2 = Math.Pow(sqrtF2, 2);

bool isFibonacci = (squareF1 == f1) || (squareF2 == f2);

if (isFibonacci)

Response.Write("The given number is a Fibonacci Number");

else

Response.Write("The given numbernot a Fibonacci Number");

}

When we check the number 5 is Fibonacci number or not.

IsFibonacciNumber(5)

OUTPUT:

**The Given number 5 is a Fibonacci Number.**

IsFibonacciNumber(14)

OUTPUT:

**The Given number 14 is not a Fibonacci Number.Thanks**

**Vijendra Singh**

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