# THE FIBONACCI SEQUENCE AND PINEAPPLES

## Believe It or Not

### By: John Catlan

Look at any plant - tomato, strawberry or pineapple, count the number of petals, or the way the leaves are arranged. You will find them set out in pairs, threes, fives, eights or thirteens, but never fours. Plants don't like four.
Plants stick to numbers in the series 1,2,3,5,8,13,21,34 where each number comes from adding the previous two together. The series is called The Fibonacci Sequence. Mathematicians love this string of numbers, as do plants. You will find these numbers in the five seed chambers you find when you cut across an apple, or the 34 or 55 spiral whorls in a sunflower head. We do not have four-leafed clover or a four-leafed anything else.

### PHYLLOTAXIS; ARRANGEMENT OF LEAVES ON STEM.

In the following, note how the Fibonacci Sequence seems to rule: the flowers of a pineapple and thus bromeliads have three petals.
When I seriously started to look at the shape of Neoregelias and what made the shape appealing and what was right for the plant, the work on pineapples was the bench mark to copy. Once you understand how leaf shape is formed you do not have to strip a plant, you can line up leaves and count, but I will explain in detail. The leaf phyllotaxy can be determined by removal of the leaves and marking the growth bud at the base of the leaf then noting the number of leaves which have to be removed before another leaf bud appears on a line on the stem extending vertically above the first number bud, and also noting the number of spirals that have been made around the stem. We find the leaf phyllotaxy is 5/13. The five is the number of spirals around the stem and thirteen the number of leaves removed in the five spirals until another bud, the fourteenth is found directly above bud number one.

When a pineapple is formed hormones change the phyllotaxy from 5/13 of the leaves to 8/21 of the fruit. In normal fruit the number of rows of each type of spiral is constant, there being eight of the long gently sloping rows and thirteen of short steep ones.

The fruit hormones cuts out and the phyllotaxy changes from 8/21 of the fruit to 5/13 of the leaves abnormalities in fruit and top development, such as double fruit, fan tops, multiple tops are the results of irregularities in these hormone driven phyllotaxis change.

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