Casa di Mir Summer Mathematics: Adventure #9

Fibonacci Nature Walk

Summer provides many opportunities to reconnect with nature. Did you know that, even on a nature walk, there is mathematics all around you? Grab your camera and put on your counting hat for a safari to find the numbers of the Fibonacci sequence.

The Fibonacci Sequence. The sequence of numbers named for Leonardo of Pisa (circa 1175-1250, later known as Fibonacci) was studied by Indian mathematicians as early as 200 BCE. The first two numbers in the sequence are 1 and 1. Each subsequent number is obtained by adding the last two numbers up to that point.

 

Fibonacci Scavenger Hunt. The numbers in the Fibonacci sequence occur surprisingly often in nature. The ideal nature walk for a Fibonacci scavenger hunt is one that includes a wide variety of plant life. As you wander along, be on the lookout for three types of Fibonacci finds:

  • Flower Petals. Count the number of petals on flowers and you’ll find that the petal count is often exactly or nearly one of the Fibonacci numbers. For flowers with many petals, it is helpful to put a dot on one petal with a permanent marker to help in the counting process.

  • ​​Leaf Sections or Lobes. Count the number of sections or lobes of leaves and you’ll find that this count is often exactly one of the Fibonacci numbers.
  • Pine Cone Spirals. Many pine cones have brachts that are arranged in spirals. Look at the stem end of a pine cone. Use a permanent marker to color the brachts in one spiral from the stem to the outside edge. (You can see a drawing of what this would look like on this blog post at Curiosa Mathematica.) Then count the number of such spirals. Often, this is one of the Fibonacci numbers. Now, look again at the pine cone and notice that there are spirals in the other direction!  Use a permanent marker to color the brachts in one of these spirals in the other direction and then count them. Is the number of spirals in the other direction the same as the number of spirals in the first direction? How are those numbers related to each other?

For a fantastic and accessible deep dive into the mathematics behind spirals in nature, see Vi Hart’s three-part series of videos titled Doodling in Math Class: Spirals, Fibonacci, and Being a Plant.

Honey Bees. If you spied honey bees on your nature walk, then you encountered another instance of the Fibonacci sequence that isn’t as visible as with plants. Male bees result from unfertilized eggs whereas female bees result from fertilized eggs. This makes the ancestor tree of any bee very interesting. In particular, if you count the number of bees in each generation of a male bee’s ancestors, starting with the male bee itself, you’ll discover the Fibonacci sequence! A great one-page illustration of this is available from University Child Development School. Have your kids re-create the ancestor tree and add on a couple more generations to verify that the Fibonacci sequence really does model this real-world phenomenon.

Whether in your garden at home or out among the redwoods, the Fibonacci sequence is never far from discovery if you have the inclination to stop, notice, and wonder. Enjoy your explorations.

About the author: Trisha Bergthold has been the middle school math teacher at Casa di Mir Montessori School since 2014. She holds a PhD in mathematics with emphases in curriculum and pedagogy. Prior to her work at Casa di Mir, she designed curriculum for kindergarten through college level. She also taught university-level mathematics courses for sixteen years.

A special thanks to teachers Tyler Bourcier and Pheroza Doshi for joining Trisha in a trial run of this activity, and to Tyler for taking the photographs.