Lesson 2 - Page 3



Fibonacci Sequence

The Fibonacci Sequence is made up of the Fibonacci numbers.  This number series was named for Leonardo of Pisa, son of Bonacci (figlio (son in Italian) of Bonnacci) or  Fibonacci (1180-1228). He first wrote about the sequence in Liber Abaci by giving the solution to how many rabbits can breed in a year.   The French mathematician Edouard Lucas (1842-1891) named the Fibonacci sequence in honor of the inventor.

Fibonacci started to think about how many pairs of rabbits could be breed in 12 months.  In order to figure it out, Fibonacci had to establish some rules.  In the first month there is just one newly born pair of baby rabbits. So he averaged that in one month a pair would have two baby rabbits and it would take 1 month for the rabbits to become an adult and have babies of their own.   None of the rabbits could die during the year.  He discovered a sequence that is based on the idea that each number is the sum of the two preceding numbers. 

So you start with two pairs (1 and 1), then you add the preceding two numbers so you get  the total number of rabbits each month.  The number of rabbits  is derived from 1 (starting), 1=(0 +1)  (this gives us 1 pair); 2=(1+1), 3=(1+2), 5=(2+3), 8=(3+5), 13=(5+8),  21(8 +13), 34(13 + 21); 55 (21 + 34), 89 (34 +55), 144 (55+89).  So in one year, there would be  144 rabbits.

The Fibonacci Sequence is 1,1,2,3,5,8,13,21,34,55,89,144.  If you graph these numbers as squares, you get an interesting configuration called the Golden Rectangle.  If you draw a line from corner to corner you get what is called the Golden Spiral, which we see in nature.  The Nautilus shell is a good example of this figure. 

Click on drawings for example

Squaring the Fibonacci Numbers an
d you
build a rectangle arrangement

Draw a line and you get a golden spiral


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