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Fibonacci
number patterns occur so often that we often hear the phenomenon referred
to as a "law of nature".
If we
examine flowers, we would find that the number of petals on a flower is
often one of the Fibonacci numbers. For example:
One- and two-petalled flowers are not that common. Three- and
five-petalled flowers are more common, and there are quite a number of
well known species with eight petals. Thirteen-,
twenty-one, and thirty-four-petalled flowers are also very
common. I'll bet you never thought how much the number
of petals differed on flowers, and now we can see that there is a relation
between the number of petals these flowers have - the Fibonacci
sequence!
The association of Fibonacci numbers and plants is not restricted to
numbers of petals. Dr. Jill Britton's website explores more
nature connections to the Fibonacci sequence:
Fibonacci
numbers can also be seen in:
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SEED
HEADS
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PINE
CONES
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VEGETABLES
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| Source of Images: Knott,
R.. "The life and numbers of Fibonacci ." The life
and numbers of Fibonacci . Millennium Mathematics Project. 27
Aug 2006 <http://www.pass.maths.org.uk/issue3/Fibonacci/index.html>. |
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Fruits
If
you cut a fruit or vegetable you will often find that the
number of sections is a Fibonacci number:
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Apples have 5
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Bananas have 3
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| Source of images and
Information: "Plants."
Phi - The Golden Number. 27 Aug 2006 <http://goldennumber.net/plants.htm>. |
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Nature
Research Task:
With
your parents' permission, find two fruits or vegetables in your
home. An Alternative would be to examine a flower as one of
your items. Use an index card to record your
results. These will be posted later on the Fibonacci
Blog.
For a Banana:
Count how many "flat" surfaces it is made from -
is it 3 or perhaps 5?
With your parents' assistance peel the banana and then cut
it in half (as if breaking it in half, not lengthwise) and look
again. Surprise! There's a Fibonacci number.
For a Cauliflower or Broccoli:
First
look at it.
Count the number of florets in the spirals on your
cauliflower.
The number in one direction and in the other will be Fibonacci
numbers, as we've seen here.
Then, take a closer look at a single floret (break one off
near the base of your cauliflower). It is a mini
cauliflower with its own little florets all arranged in spirals
around a centre.
If you can, count the spirals in both directions. How many are
there? Counting them again shows the Fibonacci number.
For
a Flower:
What
is the name of the flower? Note if the number of
petals is a Fibonacci Number. How about the number or
organization of leaves? The seeds? If possible, find
an image of the flower online and post it as well.
Post
details about your investigation your notes on the Fibonacci
Blog. Share your observations with your classmates.
Then respond to at least three (3) fellow classmates' postings,
using Grade 4 ELA standards.
Due Date: Tomorrow a.m.
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