|
|
Article: A family of sequences.
- Article from:
- Australian Senior Mathematics Journal
- Article date:
- January 1, 2009
- Author:
CopyrightCOPYRIGHT 2009 The Australian Association of Mathematics Teachers, Inc. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
|
Perhaps a business colleague threw out a challenge. The year: around 1200. The place: Pisa. The challenge: Calculate how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on.
The question and its solution found its way into the book Liber abaci by Leonardo of Pisa (known as Fibonacci), completed in 1202. It gives rise to the Fibonacci sequence.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
More recently, a colleague of mine issued the challenge: Prove that the sum of the squares of any two consecutive terms of the ...