Sunflowers are applied mathematicians at heart

Disk florets of yellow chamomile (Anthemis tin...

Disk florets of yellow chamomile (Anthemis tinctoria) with spirals indicating the arrangement drawn in. (Photo credit: Wikipedia)

I have known about the beauty of the pattern of seeds in the heads of sunflowers for a long time now, but still stare in wonder just as I did when I saw it the first time. You count the number of spirals in each direction and find that they are two consecutive numbers in the Fibonacci Sequence.

I recently heard that the pattern also includes the Golden Angle. This is when you divide up 360 degrees into two angles in the Golden Ratio. The smaller angle is the Golden Angle which is irrational and measures 137.508… degrees. The seed pattern is formed by seeds being ‘fired’ from the centre of the flower head outwards one at a time. The angle that each seed heads off from the centre when measured from the last one is the Golden Angle.

For a bit of fun I thought I’d write a computer simulation of this procedure to see if I could replicate the pattern. I then also changed the angle of consecutive seeds to plus and minus one degree from the Golden Angle to see how sensitive the pattern is to the angle. The results are surprising!

It seems as though the seed pattern is extremely sensitive to the angle that the seeds are released! Therefore we must conclude that sunflowers are great admirers of the beauty of mathematics! They are applied mathematicians at heart, putting their knowledge into a wonderful real world application!


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Tweeting using the Golden Ratio

It’s well known that many architectural designs base their proportions on the Golden Ratio including the Egyptian Pyramids, the Parthenon, the Notre-Dame of Laon cathedral etc and that the ratio appears all over the natural world including the length to width of the DNA helix.

However, I bet you didn’t know that the Golden Ratio has worked it’s way into Twitter! Like it or not, social media is here to stay and it seems our pupils consider sending out a tweet or status update to be as normal as phoning, texting or IM-ing a friend. If you are looking for another example of the aesthetic qualities of the Golden Ratio then look no further than the design of the new-Twitter! The proportions of the various sections of the page are in the golden ratio:

Twitter homepage designed using the Golden Ratio- Picture from

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The Fibonacci Sequence in nature

SunFlower: the Fibonacci sequence, Golden Section

Image by lucapost via Flickr

As the end of term draws near we are all looking for lessons to inject a bit of fun into the last two weeks of term. I need some display work for my classroom so am getting the pupils to create posters about the famous mathematician Fibonacci.

After introducing the Fibonacci Sequence, I then showed the pupils this presentation which shows where it turns up in nature. We also talked about Fibonacci and how he was actually called “Leonardo of Pisa” and how he brought the base ten number system to Europe. We also drew some Fibonacci spirals and then looked at the shape of a Nautilus.

The pupils were astounded by the presentation and it really inspired them. One of them even asked me “did God use the Fibonacci Sequence when he built all the universe?”! One of them then said “Sir, we are made up of Fibonacci numbers too; we’ve got 1 nose, 2 hands, 5 fingers etc…”. He then said he was going away to look at animals and see if they have numbers of limbs and features that were Fibonacci numbers. Isn’t this what we are aiming for in our pupils? Initiative, enquiry, curiosity, questioning. Great!

They have all gone away super keen to find out more about the great man and to gather things to put on their posters next week.


Pure inspiration- nature by numbers

This has to be one of the very best videos I have ever seen to show the beauty and power of maths. Just imagine all the ways you could use this to inspire the kids.

No further comments needed!


Download the movie in 3GP file format here.

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Download the movie in MP4 file format here.