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Lesson 3-1

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Saved by Pete Anderson
on March 28, 2010 at 9:29:15 pm

Unit Three:

Nature

Lesson 3-1:

Form, Pattern, and Number

Objectives:

to recognize geometric forms and patterns found in nature
to learn of the Fibonacci Sequence
to learn and explore example of Fibonacci numbers found in nature

Warm-Up Activity: Behold Nature's Mathematical Beauty

On the following web site, view the photos of snowflakes. There are 3 galleries.
Watch the slideshow below of Mr. Anderson's Geometry of Nature photo gallery. Because it is from Flickr.com, you may not be able to see this at school.

Activity #19: Form and Pattern

Part One: Form

For the purposes of this activity, let's define "geometric form" as that which demonstrates [clearly] lines, polygons, circles and/or spirals in part or in whole. Find two examples of "geometric form" in nature either from the web or with your camera [bonus points for using your camera]. Upload your pics to your wiki folder and add them to the following page: Geometric Form in Nature. Include the name of the object and the "geometric form" it represents. Use the example to the right as a guide.

Name: Rex Begonia

Form: Spiral

Part Two: Pattern

For the purposes of this activity, let's define "geometric pattern" as repetition of "geometric form". Therefore, if it contains a "geometric pattern", it must contain a "geometric form". Find two examples of "geometric pattern" in nature either from the web or with your camera [bonus points for using your camera]. Do not use the same pictures from activity one. Upload your pics to your wiki folder and add them to the following page: Geometric Pattern in Nature. Include the name of the object and the "geometric pattern" it represents. Use the example to the right as a guide.

Name: Sedum

Form: repeated spiral design clockwise and counter-clockwise

Rubric:

Prep: BBC progam "5 Numbers" with Simon Singh

Listen to the 3rd installment of this series: "The Golden Ratio".
Listen to BBC program (13:52)
As an option you may wish to "Right Click" the link above and choose "Save Target As".
If you want more, visit the programs web site.
- 5 Numbers: Zero, Pi, Phi, i, infinity

Activity #20: Leonardo of Pisa (in a spreadsheet)

Directions:

Download the spreadsheet for this activity.
Using formulas, create the following:
- an additive sequence
- division of terms of the additive sequence
- a sequence that alternates between "plus 1" and "reciprocal" of the previous term.
- Sum of n terms
- Sum of 10 terms divided by 11
- Squared Terms
- Term1*Term2 + Term2*Term3 + Term3*Term4 + ...
Watch videos for help.
Video: Additive Sequence
Upload your spreadsheet file to your wiki folder and create link on your wiki page that will open the file.

Rubric:

For more Mathematic Magic with Fibonacci numbers, look at this

web site. My personal opinion is that some of this crosses the line into fanaticism.

Now "skim through" the web site below. It's a fairly exhaustive list on the findings of Fibonacci Numbers in Nature.

Activity #21: Discussion

Is nature goverened by a mathematical concept like the golden ratio?
Is the Fibonacci Sequence a mere consequence given that it doesn't apply to all living things?
Is there some "middle ground"?

Use the comment section below to ask the teacher questions or leave a comment about this lesson.