MATHEMAGICA
Interesting mathematical snippets from
the history and practice of mathematics
September/October 1998
More
about Fibonacci and his numbers
Fibonacci, or Leonardo of Pisa, lived around
1175 to 1250
Fibonacci numbers occur in a wide
range of natural systems. If you are a mathematics teacher exciting lessons
can be built around the Fibonacci sequence.
Collect some of the following objects: Pine
cones, cacti of the globular variety, seed heads of plants such as "Cuckoo
Pint" with a columnar array of seeds, fruits of proteaceous plants
eg Leucospermum or Banksia (you can rub off the floral remains to leave
the central core), sunflower seed heads and pineapples.
All of these have parts arranged
in a triplet of easily discernible spirals. The numbers of spirals are
members of the Fibonacci sequence usually ranging from 5 to 21. It pays
to choose your specimens carefully because any environmental disruption
to growth can realign the succeeding spirals, making it difficult to count
across that boundary.
Hand out a variety of those objects to your students and ask them to count
the spirals. They may need some assistance and markers (felt-tip markers
or small sticks eg matchsticks) to locate the starting point. Record their
results on a blackboard or overhead display. As the results mount up the
preponderance of fibonacci numbers becomes obvious and some students even
recount more carefully and adjust their results. (They should not alter
their numbers to fit - deviations do arise naturally).
Ask them to look for some relationship between the numbers and then to
predict more numbers in the series. You can talk about the marvellous occurrence
of Fibonacci numbers in the flora of the world and speculate on whether
it applies to animals. Then introduce the "Pig Game"
