The Library

thelibrary.org Springfield-Greene County Library District Springfield, Missouri
Science

Key Concepts: Mathematics - Fibonacci Numbers

What is it?
 
The Fibonacci sequence of whole numbers is:
 
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,...
 
Have you figured out the pattern? What is the next number in the sequence? Answer below
 
The sequence is widely known for its many intriguing properties. Here are but a few. 
                1+1=2
                1+1+2=4
                1+1+2+3=8
                1+1+2+3+5=12
                1+1+2+3+5+8=20
                ....
Origins
 
Leonardo of Pisa (also known as Fibonacci) introduced the sequence to Western European mathematics in his 1202 book Liber Abaci. The numbers had been previously described in Indian mathematics. In the book he considers the growth of an idealised (biologically unrealistic) rabbit population, assuming that: a newly-born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year?
 
Conclusion: At the end of the nth month, the number of new pairs of rabbits is equal to the number of pairs in month n-2 plus the number of pairs alive last month. This is the nth Fibonacci number.
 
For more information about History of Mathematics
 
Books
Links

Answer: 4181

Resource: Henderson, M., Baker, J., & Crilly, T. (2009). 100 most important science ideas : key concepts in genetics, physics and mathematics. Buffalo, N.Y. : Firefly Books.
 

Find this article at