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.

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!

Websites:
Everything you wanted to know about Fibonacci
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

Teacher Resources for Enrichment
http://www.mensaforkids.org/lessons/fibonacci/mfklessons-fibonacci-all.pdf\

How do I count the spirals? Museum of Mathematics Website article
http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/

Science and Math in Sunflowers
http://news.sciencemag.org/math/2013/06/scienceshot-sunflowers-do-math

Videos:
http://www.youtube.com/watch?v=wTlw7fNcO-0

http://www.youtube.com/watch?v=ahXIMUkSXX0 (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!

http://www.youtube.com/watch?v=lOIP_Z_-0Hs&feature=youtu.be (Part II, more plants and sequencing and WHY plants have this sequence).

http://www.youtube.com/watch?v=kkGeOWYOFoA (gorgeous video)

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