Ana’s Math Blog
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In class today we worked on the Menger Sponge (actually, a 2D version called a Sierpinski Carpet).  Create a spreadsheet for calculating the area at any iteration.  Create a graph that goes to the 15th iteration.  Then, write a paragraph about what you notice.

Your paragraph should be clear and mathematical.

• Discuss general trends you notice and support them with mathematical evidence.
• Explain exactly how much the pattern changes by each time.
• Compare what you know about this pattern to what you observed about the Sierpinski Gasket and/or any other patterns.
• Check for correct spelling or grammar.

The Sierpinski Gasket

Use excel to create a spreadsheet and a graph for representing the area of the Sierpinski Gasket.  Then write a paragraph about what you notice.Your categories will be different from the ones you used for the Koch Snowflake - think carefully about what you need to know to calculate the area at each iteration.  Remember to proofread your paragraph before you turn in your assignment - I shouldn’t see any spelling or grammar errors.  Also, please remember the proper heading for you work! 

Koch Squared

Create a perimeter and area spreadsheet for the square version of the Koch snowflake. Use the “chart” tool to make a graph of each. Observe the similiarities and differences with the original snowflake. Write one paragraph about what you notice about how the perimeter grows and one paragraph about how the area grows.

Be careful! There are many similarities with the original snowflake, but the formulas are not identical. Be thoughtful. Use the diagrams you started in class! See me soon if you need help.

Koch Snowflake Area & Perimeter: Report on solution

You are revisiting the two questions I originally asked you about what would happen to both the area and the perimeter as the number of iterations approaches infinity.  Your answers should be thoughtful and well-supported by the data in the tables and graphs.  The writing should also be checked for spelling and grammar.  The final assignment should include:

•  (Optional cover page)
• Perimeter spreadsheet & graph
• Area spreadsheet & graph
• 1 page of writing addressing the two questions:

1.     What happens to the perimeter as the number of iterations approaches infinity?
2.     What happens to the area as the number of iterations approaches infinity?

Due Wednesday:

Use excel to create two spreadsheets: one for the perimeter of the Koch Snowflake and one for the area.

The perimeter, which we started in class, should have the following column headings: Iteration, Number of segments, Size of segments, Perimeter.  The area spreadsheet should have the headings: Iteration, Number of new triangles added, Size of each new triangle, Total new area added, Total Area.

Have the spreadsheets printed out for our class and be ready to explain the formulas you wrote.  You can work together, but you must be able to speak for your own work.