Pine cones show the Fibonacci Spirals clearly. Here is a picture of a pinecone seen from its base (sorry the quality is a bit poor) and another with the spirals emphasised: red in one direction and green in the other.[Click on the images to enlarge them.]
• How many red spirals are there?
• Collect some pine cones for yourself and count the spirals in both directions.
A tip: Soak the cones in water so that they close up and counting the spirals is easier.
a. Does the number of spirals differ for each kind of tree/cone or not?
b. Are all the cones identical in that the steep spiral (the one with most spiral arms) goes in the same direction?
• What about a pineapple? Can you spot the same spirala pattern? How many spirals are there in each direction?
^^^ You will occasionally find pine cones with do not have a Fibonacci number of spirals in one or both directions. Sometimes this is due to deformities produced by disease or pests. For instance, a large collection of pine cones of different kinds of Californian pine cones was studied by Brother Alfred Brousseau and reported in The Fibonacci Quarterly vol 7 (1969) pages 525 - 532 in an article entitled Fibonacci Statistics in Conifers. He also found that there were as many with the steep spiral (the one with more arms) going to the left as to the right.
^^ Pineapples and Fibonacci Numbers P B Onderdonk The Fibonacci Quarterly vol 8 (1970), pages 507, 508.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More..
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