What

=What is the Fibonacci sequence?=

The first 15 number in the fibonnaci sequence are 1=1 2=1 3=2 4=3 5=5 6=8 7=13 8=21 9=34 10=55 11=89 12=144 13=233 14=377 15=610 To work out the next number in the sequence we need to add the number before it and the number two before it, for example, the 8th number we need to:

Add the number before it in the sequence, which is 13, and then the number two before it in the sequence, which is 8. The answer is 21, which means the 8th number in the fibonacci sequence is 21. This can be expressed as a formula, n(the number) + n1( the next number) =n2( the number two after the the number).

The fibonacci sequence can be found in Pascals triangle(See FAQ). For example to the 9th number in the fibonacci sequence can be found in the triangle. Add up the bold numbers and which add up to 34 the 9th number in the sequence The same angle in this line can be applied on the triangle in different places to find a number in the fibonacci sequence.

When you divide a number in the fibonacci sequence by the number in the sequence before it, the number you are left with is 2/1= 3/2= 1.5 5/3= 1.66667 8/5=1.6 13/8=1.625 21/13=1.6153 34/21=1.619 55/34=1.6176 89/55=1.6181 144/89=1.6179 233/144=1.618 377/233=1.618 610/377=1.68 As the number gets bigger a pattern emerges, the number which starts to show up is always approximately 1.618. This pattern is called the golden ratio. This ratio turns up in nature, we measured a finger and the longest bone was 60mm the middle bone was 35mm and the shortest bone was 25mm when we divide the longest by the middle the answer is 1.714 and the middle by the shortest is 1.4. Both of these numbers are pretty close to the golden ratio. The only reason that they are slightly is off because of the accuracy of our measurements. The Greek letter of Phi is used to denote the golden ratio.

Fibonacci sequence can be applied to problem solving If we can only make milk out of 1L or 2L how many different ways could we make different amounts of milk(1L,2L,3L, 4Letc) if the order of the sizes of milk it is important. 987 milk ways