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Fibonacci fruit

By Mike, 16 January 2013 Activity

Pineapple scales form diagonal rows.

Pineapple scales form diagonal rows.

Having trouble finding a four-leafed clover? This activity explains why! If you’re getting ready for some gardening, keep this activity in the back of your mind as you marvel at Mother Nature’s mathematics.

You will need

  • A selection of flowers
  • A mature pineapple

What to do

  1. Count the petals on each of your selection of flowers. What numbers do you get? Do any have four petals? Seven? Nine? Ten?

    Few flowers have four petals.

    Few flowers have four petals.

  2. Look at the ‘scales’ making up the skin of your pineapple. Notice how each scale sits at a slight angle and looks roughly like a pentagon, with each flat side touching the flat side of another scale. Also see how they make up diagonal rows or lines that encircle the pineapple.
  3. Find one of these diagonal lines and count its scales. Don’t forget to include the ones at the very top and very bottom of the pineapple.
  4. Find another line running diagonally around the pineapple the other way. How many scales are in this line?
  5. Count five examples of each line. What numbers are you getting?

What’s happening?

Some flowers appear to have six petals but they actually have three petals and three sepals.

Some flowers appear to have six petals but they actually have three petals and three sepals.

Chances are you’ll find examples of flowers with one, three, five, eight, thirteen or even twenty-one petals, but won’t find many with four, six, seven, nine or eleven petals. As for the pineapple, with a few exceptions, you will find one of the rows will have thirteen scales, while the other will usually have twenty-one.

What is so special about these numbers? They are called ‘Fibonacci numbers’, and seem to come up often in nature, whether in the seeds of sunflowers or pinecone scales. It’s easy to work out what the sequence is – simply add together the previous two numbers to work out the next in line.

For instance, start with 1. Add 1 and 0… and get 1 again. Add 1 and 1, get 2. Add 1 and 2, and get 3. Then 3 and 2 make 5.

Count the scales on a pineapple.

Count the scales on a pineapple.

The sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … and so on.

Of course, nature is full of small variations (that’s how evolution works!), which is why you’ll occasionally find a flower with four or six petals, or count a line of 14 or 12 scales on your pineapple. Four leafed clovers do occur, yet nature seems to follow Fibonacci numbers, which is why you’ll find far more clover stems with three leaves.

Applications

While nature might not be able to count in the same sense you can, numbers often indicate an underlying pattern which is determined by a natural law.

There are many possible reasons that could make these numbers the most useful and efficient for the plant, such as a combination of the angle of new shoots, growth and the amount of available space.

Of course, it is possible the numbers might not necessarily be the result of a particular law, or we are just seeing this particular pattern because that is what we are looking for (called ‘confirmation bias’). For example, many believe the shell of the nautilus follows a pattern called the ‘golden spiral’, a shape which also relies on Fibonacci numbers. While it is true the spiral does follow a mathematical rule, allowing the mollusc to grow without changing its shell’s shape, it’s not quite the same as the golden spiral.

So while it might be nice to think Fibonacci numbers are everywhere in nature, we do need to take care not to see them where they may not really be.

More information

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