Algebra

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Special Sequences: Fibonacci Sequence

The Fibonacci Sequence is a special mathematical sequence which has significance in both natural and man-made structures.

The Fibonacci Sequence is a special type of sequence where each term is the sum of the previous two terms.

The first few terms of the Fibonacci Sequence are given below. Notice that each term adds together the previous two terms.

$1,1,2,3,5,8$

Here is the Fibonacci Sequence illustrated

To make each new term, we add together the previous two terms.

This is another Fibonacci-type sequence

It follows the same pattern, where each term is a sum of the previous two terms.

Which value comes after 6?

The next value would be 10

The previous two terms are $6$ and $4$ , and $6+4=10$ .

What value comes after 10?

The next value is 16

This time, the previous terms are $10$ and $16$ , and $6+10=16$ .

Interestingly, this relationship underlies both man-made and natural structures. It is the sequence which creates the spiral seen in things like hurricanes, galaxies and seashells.

The spiral looks like this

Notice that there is a grid made of many individual squares. The sides of each individual square are made of Fibonacci numbers, which are each labelled within the related square.