## What is Fibonacci Series?

Fibonacci series is the sequence where the first two numbers are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two e.g. 0, 1, 1, 2, 3, 5, 8 etc.

The Fibonacci sequence is named after Italian mathematician Fibonacci, although the sequence had been described earlier earlier as Virahanka numbers in Indian mathematics.

Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences.

The Fibonacci numbers are important in the computational run-time analysis of Euclid’s algorithm to determine the greatest common divisor of two integers: the worst case input for this algorithm is a pair of consecutive Fibonacci numbers.

#### Recognizing Fibonacci numbers

The question may arise whether a positive integer x is a Fibonacci number or not. This is true if and only if one or both of or is a perfect square.

### Fibonacci Series without recursion:

<?php
$term = 10;
$num1 = 0;
$num2 = 1;
for ( $i = 0; $i < $term; $i++ ) {
if ( $i <= 1 ) {
$result = $i;
} else {
$result = $num1 + $num2;
$num1 = $num2;
$num2 = $result;
}
echo ' ' . $result;
}
?>

### Fibonacci Series using recursion:

<?php
function fibonacci($n)
{
if ( $n == 0 ) {
return 0;
} else if ( $n == 1 ) {
return 1;
} else {
return ( fibonacci( $n - 1 ) + fibonacci( $n - 2 ) );
}
}
$term = 10;
for ( $i = 0; $i &amp;lt; $term; $i++ ) {
echo ' '.fibonacci($i);
}
?>

Output: 0 1 1 2 3 5 8 13 21 34

#### Fun fact

Fibonacci Day is November 23rd, as it has the digits “1, 1, 2, 3” which is part of the sequence. So next Nov 23 let everyone know!