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Non-linear Pattern Web Quest

on June 25, 2012

For my web search, I googled the following two combinations:

“Fibonacci” and “Phyllotaxis” and “Prime Numbers”

“The Golden Ratio” and “Pentagrams”

I’ve heard of the Fibonacci Sequence and briefly introduce it when talking about patterns/sequences in Algebra class but was unaware of all of the applications of this sequence in nature and art.  Below are a few interesting websites that I located from my searches:

Good website on the biography of Leonardo Pisano (Fibonacci): http://www.lifeinitaly.com/heroes-villains/fibonacci.asp

Website visually demonstrating phyllotaxis spirals: http://maxwelldemon.com/2012/03/18/prime-phyllotaxis-spirals/

Website giving lesson ideas to teach the golden ratio and its importance: http://www.ldlewis.com/Teaching-Mathematics-with-Art/golden-ratio-instructions.html

  • Were there ideas or concepts you were not familiar with? What were they?  I was unaware of all of the applications of the Fibonacci sequence, such as the golden ratio and its use with converting miles/kilometers and its use in art/architecture because of the number phi and Pascal’s Triangle and its use in probability.
  • What images did you find particularly striking?  I really enjoyed reading about phyllotaxis spirals and images associated with them and their implications in nature and how different degrees produce different spirals.
  • Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?  I love flowers and plants and my husband brings flowers to me on a weekly basis and I will now have a new appreciation of them and their patterns.  What used to seem “random” is not and I will now look at them in closer detail to count petals and explore their nonlinear patterns.
  • How can you adapt this webquest activity for your classroom?  Being a cyber teacher, my students have access to the Internet with a click of their mouses and I think that this year, when introducing the Fibonacci sequence, I will break students into groups and have them spend 15 minutes searching the internet for applications of this sequence.  I will have some students research the golden ratio and others research phyllotaxis spirals and others research Pascal’s Triangle.  I will then have students report back into the LiveLesson and share the sites and information that they’ve found so that they can see some real-world applications of nonlinear patterns.

One response to “Non-linear Pattern Web Quest

  1. jgehr says:


    Your ideas for adapting the webquest for you students is an excellent idea. Having your students research the topics you mentioned will add a new element to your lessons. There are some excellent resources on the web and your students will enjoy exploring them.


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