THE FIBONACCI SEQUENCE
The sequence arises from a
problem posed by Fibonacci in 1202:
Start with one pair of rabbits in a perfect environment, and suppose
that:
- No rabbit dies.
- The initial pair of rabbits take one month to
mature.
- They produce a new pair at the end of the second
month and at the end of each subsequent month.
- Each new pair becomes adults after a month and like
the first pair produce offspring in the same pattern.
How many pairs of rabbits are
there at the end of the first year?
Investigate the Fibonacci
sequence by undertaking the following tasks:
- Answer Fibonacci’s original rabbit question and
describe what is now known as the Fibonacci sequence.
- Find at least three mathematical relationships that
are satisfied by the Fibonacci sequence. For example, if Fn is
the nth number in the Fibonacci sequence, then F1 + F2 +
F3 + … + Fn =
Fn+2 – 1.
- Describe where the Fibonacci numbers occur in
nature.
- Explain what the golden ratio is and how it is
calculated.
- Give some examples of how the golden ratio is used
in art, music and architecture.
You can access many web sites on
the Fibonacci sequence using common search engines.
Developed by Susan Worsley.
http://www.maths.uq.edu.au