Fibonacci Sequence
Fibonacci was an Italian mathematician who was born in Pisa in 1170.
The name Fibonacci is short for filius Bonacci which means son of Bonacci. Fibonacci popularised the decimal number system that we use today in his book called Book of Calculation. In this book he also introduced a sequence of numbers that came to be called the Fibonacci Sequence.
In the Fibonacci Sequence, you start with the numbers 0 and 1 and add these together to make the next number. You then keep adding the two previous numbers to create the next number. The first eleven numbers in the sequence are:
We could label the first number as n = 1, the second as n = 2 etc. We can label the value of the sequence when n = 1 as x1 and the value when n = 2 as x2 and so on. So x10 = 34, for example.
x1 = 0, x2 = 1, when n > 2 then the value of the Fibonacci sequence is the sum of the two previous values. We can write this as xn = xn-1 + xn-2
For example x10 = x9 + x8 = 21 + 13 = 34
Here are the Fibonacci numbers for n = 2 to 7 represented by squares. The squares have sides of length 1, 1, 2, 3, 5, 8
We can arrange these squares in a pattern, like so.
We can draw a spiral by drawing a curve within each square.
Fibonacci numbers and the curve shown above appear throughout nature. In the spirals of seeds on a sunflower, the number of petals on flowers, the spiral of shells, the shape of hurricanes and the spiral arms of galaxies.
