Wednesday Wonderment – pt 11

Fibonacci is everywhere!

There are certain aspects of Nature that inspire amazement when we look at them and even greater amazement when we analyze them even deeper.

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Fibonacci’s Flower

The mighty sunflower is an amazing little piece of mathematical design, when we analyze the spiral shapes in which the seeds are laid out.  I think most of us have heard of Fibonacci numbers: the sequence 1, 1, 2, 3, 5, 8, and so on, so that each number is the sum of the last two.  When looking at the spiraling shapes in cauliflower, artichoke and the sunflower floret, as seen above, we see this sequence appear in front of our eyes.

Upon analysis, we see that those spirals pack florets as tight as can be, maximizing their ability to gather sunlight for the plant. But how do plants like sunflowers create such perfect floret arrangements, and what does it have to do with Fibonacci numbers? A plant hormone called auxin, which spurs the growth of leaves, flowers, and other plant organs, is the key: Florets grow where auxin flows.  This has been modelled mathematically by researchers to demonstrate the Fibonacci spiral count is the optimal dense-packing strategy.

How to Count the Spirals


The sunflower seed pattern used by the Museum of Mathematics contains many spirals. If you count the spirals in a consistent manner, you will always find a Fibonacci number (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …). Below are the three most natural ways to find spirals in this pattern. Note that the black pattern is identical in all the images on this page. Only the colored lines indicating the selected spirals are different.
The red lines show 34 spirals of seeds.
The red lines show 34 spirals of seeds.
Choosing another slope, the green lines show 55 spirals of seeds.
Choosing another slope, the green lines show 55 spirals of seeds.
And choosing a very shallow slope, the blue lines show 21 spirals of seeds.
And choosing a very shallow slope, the blue lines show 21 spirals of seeds.

– See more about this at: http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/#sthash.XF0YpZoT.dpuf

Hope you enjoyed this bit of in-depth view of the sunflower!

 

Instant Grammar – page 26

The image on page 6 was shot on September 5, while I was waiting for my car to be serviced.  It had just rained and I sauntered over to the Panera close to the dealership to get a bit of breakfast.

A Sunny Flower on a Rainy Day
A Sunny Flower on a Rainy Day

After a (somewhat) healthy power breakfast with a cup of hot green tea, I was walking back and rather liked the sky that presented itself, so was looking for an opportunity to photograph it in some fashion.

As it happened, the dealership had planted a nice row of sunflowers along the edge of their lot to dress things up a bit.  I liked the idea of juxtaposing the sunflower against the doughnut shop and the sky; a bit of a 3-way contrast between sun and rain, as well as healthy sunflower seeds vs killer doughnuts.  A bit of finding the position to line up flower, shop and sky, and you see the result here.

I hope you enjoyed my musings about page 26 and feel free to take a look at the entire book at the following link for the softcover versionInstant Grammar 2013 by Frank Jansen or for the hardcover version Instant Grammar 2013 (Hardcopy) by Frank Jansen