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Counting spirals

By David Shaw, 16 February 2013

There’s maths in everything, even broccoli!
Image: Jon Sullivan

There are some pretty amazing patterns lurking in nature. Do a bit of arithmetic and master the Fibonacci sequence, and then see where you can find it!

You will need

Find a pinecone and draw a line along a clockwise spiral.

• Pen
• Paper
• Permanent markers or paint pens
• Pine cones

Exploring Fibonacci

1. Write down this pattern: 1, 1, 2, 3, 5, 8, 13…
2. Can you work out what the next number in the pattern will be?

Counting spirals

Draw along the other spirals that curve in the same direction.

1. Look at the base of a pine cone.
2. Look for a spiral running clockwise in the pine cone. Draw a line along the spiral with your permanent marker or paint pen.
3. Right next to that spiral, there should be another spiral, curving in the same direction. Draw along this spiral too.
4. Draw on all the clockwise spirals coming from the base of the pine cone. Count the number of spirals you’ve found.
5. Get a different coloured pen and look for anticlockwise spirals. Draw on each and then count them up.
6. Do this with several different pine cones from different trees. Do you notice any pattern with the number of spirals you find?
7. You can find these patterns in many different plants, including:
   

   Draw the anticlockwise spirals.

   • Pineapples

   • Sunflowers

   • Everlasting daisies

   • Romanesco broccoli

What’s happening?

The number pattern in the exploring Fibonacci section is called the Fibonacci sequence. To make the next number in the sequence, you add together the two previous entries. Although this pattern is made from numbers, it turns up regularly in shapes and especially in plants.

Try this activity with pinecones from different trees.

Pine cones have many scales that are roughly the same size, and that are evenly distributed around the cone. Most pine cones have scales that run in spirals around the base of the pine cone. Although it doesn’t always hold true, most pine cones have Fibonacci numbers of spirals originating form the base of the cone.

This perhaps surprising observation doesn’t mean all pine trees know mathematics. Instead, it suggests that the rules that we follow to make the Fibonacci sequence are similar to the rules that plants follow to make pine cones.

Mathematicians have shown that you can get patterns similar to a pine cone by following two simple rules:

1. Make a new scale in the middle of the cone, in the least crowded spot.
2. All scales are pushed away from the centre slightly as they grow.

This is very similar to the way many plants grow. New growth comes from a central area called the meristem, and then spreads out to allow for more new growth. Although these rules are simple, the end result appears complex and beautiful.

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