Finish using reflection and rotation to create the pinwheel pattern from the triangle we made in class.  Remember, you can use midpoints as points of reflection also – this is very helpful!

Finish finding which combinations of rotations and reflections are equivalent.  You should have two possibilities for each of the eight sections.  (Do not include R360 – it works for all of them, of course)

Create and print 2 dihedral patterns made from the “HW sample” document in my folder in Class Shared – 7th Seminar

Make 3 cyclic figures in sketchpad that you like. Bring color prints to our next class.

Investigate Pick’s Theorem

For Bounadary Points equal to 3, 4, and 5, complete tables comparing the number of interior points (Ni) to the area (A).  You can use this applet to help you – it doesn’t work well in Firefox , though.

Then write a formula that describes how those formulas change as the number of boundary-points increases.  For example, that formula should allow you to write an equation for a boundary of eleven points without having to actually test it out in the geoboard.

This is due next Friday along with your other work from the first half of the year.  This includes these assignments:

– People in a boat (1) – initial observations

– People in a boat (2) – solutions, rules and formulas

–  2D Tile Patterns (square pattern and s-pattern)

– 3D Tile Patterns (Cube, rectangular prism and pyramid)

– Grasshopper Games

– Tower of Hanoi

– Pick’s Theorem

I will return your Tower of Hanoi problems on Monday.

Use this applet to find a relationship between the number of discs (n) and the total moves (m). Your formula should NOT depend on the previous answer – you should be able to “jump” to any number of discs.