Patterns in Nature: The Fibonacci Sequence

Mathematics in Garden Club ????  

Originally written and posted on 11/5/2013.  

Today, I am reposting a blog I wrote and published in 2013 on my Garden Club Website. I am short on time and thought that this might be a piece some might enjoy. I have updated it with a few more photographs.

Fibonacci Sequence Revisited………

Once again, this year in garden club, I will be introducing the students to what is known as the Fibonacci sequence. My interest in doing this started last year, as we explored our theme of plant adaptations. Many plants exhibit a spiraling pattern in their leaves, seeds, cones, branches, and more!

The Fibonacci sequence is named after a mathematician from long ago. He noticed these patterns and was able to decode how the numbers were generated. Basically, the sequence is generated by adding the two previous numbers together.

0+1 =1, 1+1=2, 1+2=3, 2+3=5, 3+5=8,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…….etc.

What is cool about this sequence is that many things found in nature exhibit this pattern. Some of the plants or plant products that exhibit the Fibonacci sequence were introduced last year. These included:

PINEAPPLES (epiphyte unit) – exhibit Fibonacci in the hexagonal placement on the exterior of the fruit and with leaf position (harder to see)


PINE CONES (conifer unit) – exhibit spiraling patterns when viewed from the base


CACTUS (cactus unit) – spines often are placed around the exterior of the cactus in this pattern.  Succulents can exhibit this pattern too, as shown in this photo.


And this year, during October, when we explored seeds we examined the heads of sunflowers to find a great example of the Fibonacci sequence. 

SUNFLOWERS – (seed unit) – sunflower heads exhibit the sequence patterning with the seed placementpixabaysunfloweragriculture-2676644_1920

So, why am I bothering to show the students this? For one reason, it is just cool to be able to recognize how this pattern repeats itself over and over on living things! The second reason is that it makes the students think about math and patterns found in everyday life. Thirdly, is that it makes the subject of math more beautiful! And lastly, for our group, it provides some enrichment for those students who are looking to stretch their knowledge base.
It was interesting to note that none of the students in the garden club this year had heard of the Fibonacci Sequence before! The high school volunteers had heard of it but only one knew how the sequence was generated or what it applied to. This student remembered the sequencing from an advanced biology class, not a math class! Do you see the overlap here? Mathematics is an integral part of science and science is an integral part of math! You just need to be curious enough to look for the connections. They are right in front of you!  A sixth grader I know says, “Everything is math and math is everything!” Right now, I can’t find an argument for this!

So, I’d like to leave the students with the challenge of looking for the Fibonacci sequence in nature. It appears in many more places than those mentioned above. There are also some great websites and videos that apply this concept in a visual sense. Very beautiful. Wondrous, in fact! I have long been attracted to the beauty I find in my garden, but knowing there might be some rhyme and reason behind that beauty makes it all the more attractive to me. Of course, that is because I always want to know the reason “why”. Wondering “why” is exactly our garden club theme this year. And that is “why” I am spending the time to introduce this number concept to the garden club students!

As I showed the students the huge sunflower heads from our garden, I asked them to think about the relationship between the height of these plants (I asked for guesses here) and the size of the heads (most were about  12 -17 inches in diameter). Finally, I outlined the head of the sunflower with my finger and asked them to name this measurement! The answer that was most often offered as it is the perimeter. Well, yes, it is….but the perimeter of a circle has a special name! Circumference!

In the coming weeks, I’ll be interested to know what the students think the reason is (or why) this pattern of numbers exists on plants and in nature. Is it just a coincidence? Or is there a purpose behind the patterning? Visit some of the links and watch some of the videos.  See what you think! Be ready for a great discussion!

Everything you wanted to know about Fibonacci

Teacher Resources for Enrichment\

How do I count the spirals? Museum of Mathematics Website article

Science and Math in Sunflowers

Videos: (this one moves fast, but really relates it to the plants I’ve been using as examples….worth sticking it out to the end). Please don’t doodle in class! (Part II, more plants and sequencing and WHY plants have this sequence). (gorgeous video)

Pleasure Reading:
Balliett, B. (2007). The Wright 3.
Neuschwander, C. (1997). Circumference and the First Round Table: A Math Adventure.

4 thoughts

    1. It’s a no for both! Sorry. I was very immersed in math when my boys were in school – now, not so much. I know I wish I had taken more of it in school (I went through trigonometry in HS and did well in all HS math) but my trig teacher was a d_ck (sorry) and I ended up hating it because of him. Nursing, doesn’t require a lot of math (if any). Thanks.

      Liked by 1 person

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s