Non-Linear Pattern Web Quest


Fibonacci” and “Phyllotaxis” and “Prime Numbers”

Fibonacci is a simple series of numbers named after Fibonacci.  The sequence is made by adding the last two numbers to get the next number. The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21… I’ll best remember this pattern because of the spiral it can make shown in the diagram below.


Phyllotaxis refers to how leaves grow on a stem. The two main ways leaves grow on a stem are opposite and spiral.  Opposite is 2 leaves growing from the same level on the stem. Basil is the example I found in my home that grows with an opposite growth pattern.  Spiral leaves alternate at different points on the stem.  My African violets grow in a spiral. shows great photo’s of Fibonacci numbers in nature.  One example is my Shasta daisy’s having 21 petals.

  “The Golden Ratio” and “Pentagrams” 

The golden ratio refers to the idea of proportions that are pleasing to the eye.  The ratio of our forearms to our hand is an example of the golden ratio.  Pentagrams are five pointed stars that fit inside a pentagon.

The Parthenon in Greece may have been built using the Fibonacci number sequence or golden ratio. shows pictures of artists who made crop circles using pentagram designs. is a site I would like to remember if I ever need to draw a perfect 5 pointed star for quilting.  This shows two methods.  The site also uses kid friendly language to relate the pentagram to the golden ratio.

  “Fractals” and “Nature” and “Patterns”

My definition of a fractal is it’s a geometric shape that is repeated at different scales to produce an irregular shape. They are figures with lots of detail.  There are many fantastic examples of fractals in nature as seen in the following website.


1.  Were there ideas or concepts you were not familiar with? What were they?

The only term on this list I might have heard of was fractals but I would not have been able to tell you what they were.  I am amazed at how interrelated the Fibonacci and golden ratio are with math, nature, art, architecture, music and design. 

 2.  What images did you find particularly striking?

My favorite images are of fractals.  They are so intricate and interesting to look at.  I also enjoyed looking at the flowers and plants that show how leaves, branches and petals grow in spirals.

3.  Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

The following are examples of nonlinear patterns in my home.

Fibonacci:  Petals on amaryllis, pinecones, and skin on pineapple.

Golden Ratio: plaid pattern in quilt, picture frames, and photo arrangement on wall.

Phyllotaxis:  Cactus, violet, and aloe plant

Fractals: Snowflakes, ice crystals on car window, sugar crystals when making candy, fern, cut open cabbage, broccoli, and shells.

4.  How can you adapt this web quest activity for your classroom?

I think students would enjoy doing a web quest like this one.  I would assign groups different sections to research rather than the entire web quest because of the time issue. The students can share what they learned with the class.  I have found students can really take a long time when using the computers.  The idea of using the quotes is an excellent technique to narrow the search results.  I looked up pentagrams without quotes and found sites on witchcraft.


2 responses »

  1. Susan,

    You have definitely found some great resources to use in the future. Sharing your thoughts as you worked through this activity and found examples in the world around could create powerful models for your students. This definitely focuses on creating connections and constructing personal meaning for math concepts.

    Thanks for some great web sites.


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