You should review the relationship between vertices, edges and faces. You will do a short in-class assignment about it on Monday.

Can you create a map that requires five colors?  Have  friend test it out for you.  Keep in mind which techniques create graphs that use many colors.  We’ll discuss our results next week.

Due 1/24/11 (In two weeks):

A report on the Sierpinski Gasket.

Click here for some images of how the Sierpinski Gasket “grows”.

Your report should be done in either Word or Pages and should have the following:

1. The graph showing how the total area of the Sierpinski Gasket changes over 20 iterations. You will need to input data into an Excel spreadsheet in order to create this graph.

Remember the column headings you decided on in class.  They were:

Iteration / Number of triangles remaining / Size of each triangle / Total Area

Remember to use formulas for each column – don’t do each iteration by hand!

2. At least one paragraph describing what the graph shows and why.

Work for 15 minutes this week on your Koch Snowflake Report.

The report should be done in Microsoft Word or in Pages.

It must include the following:

1.  Both graphs (one of total perimeter, one of total area) – both copied from Excel.

2.  A paragraph describing each graph.

Does the perimeter/area increase or decrease?

Is it accelerating or decelerating?

What it it approaching?

Will it ever get there?  If so, when? If not, why not?

3. A paragraph that compares and contrasts what is happening to the area and perimeter.  How is this geometric object behaving? What will happen as the number of iterations approaches infinity?

POWERS OF TEN

THE MANDELBROT SET

The Mandelbrot Set is a complex fractal.  We’re starting with a simple one – Cantor Dust.  The procedure for creating Cantor Dust is to remove the middle third of each existing segment.  Then repeat.  Let’s call the length of the original ONE UNIT.

Your HW for November 8th:

• Make a table (neat & ready to be handed in) of the cantor dust through the first eight stages.

The headings of your table should be:

Stage / Number of segments / Length of each segment / Total length

For stage 1, for example, the number of segments is 1, the length of each is 1 and the total is 1.

For stage 2, the number of segments is 2, the length of each is 1/3 and the total is 2/3.

Make a note (mentally) of any patterns you see and be ready to talk about them.

• Imagine what would happen if the iterations continued to infinity.  What would the fractal look like? How big might it be? Write a few sentences about your ideas.