Alternate Activity 1: Fibonacci Numbers in Nature
Activity time: 10 minutes
Materials for Activity
- Newsprint, markers, and tape
- A whole pineapple, a pinecone or another object with a natural pattern that reflects the Fibonacci number sequence
- Leader Resource 1, Fibonacci Images
- Optional: Computer, preferably with Internet access and projector
Preparation for Activity
- On a sheet of newsprint, write the number sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
- Print out Leader Resource 1, Fibonacci Images. You may wish to make a few copies.
- Optional: Obtain additional Fibonacci images from nature, art, and architecture from books and online sources. A Google Images search for “Fibonacci images” will generate at least a dozen; make sure each truly exhibits the Fibonacci number sequence before including it in this activity. Find Fibonacci-based spiral images from nature, including a photo of a nautilus shell, on the website of the Australian Broadcasting Corporation.
- Optional: Download Leader Resource 1 to your computer, along with other Fibonacci images you can find online. Arrange to use a computer and a monitor or projector to share the images with the group.
Description of Activity
Show a natural object, such as a pinecone or a pineapple, that exhibits a pattern based on the Fibonacci number sequence. Tell the group you will pass it around and invite each participant to make one observation about the object’s apparent design.
Collect the object. Tell the group, in your own words:
In the 13th century, a mathematician named Leonardo di Pisa, later nicknamed Fibonacci, looked at lots of natural objects like this, and observed natural processes such as the number of babies rabbits had. He noticed the frequent appearance of a particular sequence of numbers.
Post the newsprint that shows a Fibonacci sequence. Point out that 1+1=2, 1+2=3, 2+3=5, and 3+5=8. Invite participants to continue building the sequence.
Pass the object again, and invite observations. See if anyone can identify the number sequence in the object. Explain:
- When you measure length or count seeds/petals in nature’s spiraling items, such as pinecones, pineapples, sunflowers, and certain sea shells (e.g., a nautilus), you will find Fibonacci numbers.
- On a stalk of broccoli, a head of cauliflower, and certain trees, if you begin at the stem and track upward, you will see the plant first branches in two, then in three, then in five, then in eight, etc.—the Fibonacci sequence.
Say, in your own words:
Many scientists and theologians believe that much of the natural world can be understood mathematically. Today we will look at the pattern of numbers Fibonacci examined, and see if we think the recurrence of this pattern in the world around us is something miraculous.
Display the images of Fibonacci sequences evidenced in nature, art, and architecture (Leader Resource 1 or your own). Invite participants to comment on the images and discover mathematical and structural patterns. Ask:
- What strikes you as awesome, beautiful, even miraculous, to contemplate?
- Do you think the order of nature is truly a miracle? Maybe some of us find nature’s dis-order, its apparent randomness, also miraculous?
- Is math itself a miracle?
- If beauty can be explained by a mathematical equation, is it still beautiful? Is beauty a miracle?
Invite participants to name additional, everyday miracles of beauty for which a scientific explanation is known. Prompt, if needed:
- The colors of a sunrise or sunset
- The blossoming of a flower
- The surface tension of water
- A rainbow
Affirm that while an unexplained event may strike us as especially “miraculous,” someday even the most awesome events we can imagine in life or nature might have a scientific explanation. Unitarian Universalists believe that the explainable can still be miraculous.
Including All Participants
Adult participants may have comments on their own experiences with Fibonacci numbers. Affirm all contributions. Yet, be mindful that adult sharing that becomes too academic can alienate younger participants. If needed, gently return the conversation to a level that includes everyone.