Fibonacci Sequence
A Fibonacci sequence is a series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.
Simple Fibonacci sequence
Generating the sequence:
Let's examine the simpliest Fibonacci series and how the sequence is generated.
Start with 0 and 1 as the first two numbers.
First number = 0
Second number = 1
Add the two numbers 0 + 1 (to get the third number) = 1
We now have:
First number = 0
Second number = 1
Third number = 1
Then add the next two numbers (number two and number 3) 1 + 1 (to get the fourth number) = 2
We now have:
First number = 0
Second number = 1
Third number = 1
Fourth number = 2
Then add the next two numbers (number 3 and number 4) 1 + 2 (to get the fifth number) = 3
We now have:
First number = 0
Second number = 1
Third number = 1
Fourth number = 2
Fifth number = 3
Then add the next two numbers (number 4 and number 5) 2 + 3 (to get the sixth number) = 5
We now have:
First number = 0
Second number = 1
Third number = 1
Fourth number = 2
Fifth number = 3
Sixth number = 5
The process can be repeated for the number of elements desired.
Here is the first ten elements in Fibonacci's sequence:
First number = 0
Second number = 1
Third number = 1
Fourth number = 2
Fifth number = 3
Sixth number = 5
Seventh number = 8
Eight number = 13
Ninth number = 21
Tenth number = 34
Crazy how they are getting larger!
Wonder what a graph of the sequence would look like?
More extension questions!
What are the next 10 numers?
How many numbers will it take before the sequence reashers or passes 1 000?
10 000?
100 000?
1 000 000?
If the number of numbers it takes to reach a higher number decreases, then will the number sequence end?
That's all ...
- More fun with Fibonacci ... see print out of computer generated first 12 numbers.
- Program in PHP that generated it.
- See Fibonacci Numbers in Nature
Enjoy!
PHP program to generate a Fibonacci sequence
<?php
//PHP code to calculate Fibonacci sequence;
$num = 0;
$n1 = 0;
$n2 = 1;
echo "<h2>Fibonnacci Sequence " . $x . "<h2>";
echo "<br>";
echo $y;
echo "<h3>Fibonacci series for the first 12 numbers!<h3>";
echo "\n";
echo $n1 . " " . $n2 . " ";
while ($num<10){
$n3=$n2+$n1;
echo($n3.' ');
$n1=$n2;
$n2=$n3;
$num=$num+1;
}
?>
Link to an html page with this program.