Activity
10: The Fibonacci Sequence
So far you have found the Golden Ratio from rectangles and
regular pentagons.
Ratios of various kinds can also be found another way – from using a
number pattern. In a sequence of numbers there is usually an obvious relationship
that connects one number to the next. This is sometimes found to be the ratio
of one number to the previous one.
In this sequence 0, 2, 4, 6, 8, 10, 12, ......... the relationship
is 'add 2' to reach the next number in the series.
Here is the pattern of Square Numbers
|
1 |
||
|
4 |
4-1= |
3 |
|
9 |
9-4= |
5 |
|
16 |
16-9= |
7 |
|
25 |
25-16= |
9 |
|
36 |
36-25= |
11 |
In this sequence the relationship could be expressed as the
[(square root of 'n') + 1] squared
There are also other connections in some number patterns e.g. in the pattern
of square numbers here you can see that the differences from one number to
the next increases in the pattern of the series of odd numbers.
The Fibonacci sequence
The following number pattern is known as the Fibonacci sequence and the numbers
are called the Fibonacci numbers.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55,............................
Can you work out how this sequence is created?
What are the next four terms?