Symmetry:  The Art of Mathematics		Hillyard/Rasmussen

Class 6 Outline

I) Construction Quiz:  GOOD JOB !!

	A) Go over Quiz

		 
II) Assignment 5 

	A) Team exercises
		1) problem 2(a), each group chose an example to share with the class on the white board
		2) do the same with 2(b)
		3) class voting on favorite
		4) look at poster board, choose your favorite 
		5) problem 3, teams decide what happened, report
		
III) Rigid motions revisited

	A) Recap of last class
	1) Combining two rigid motions M and N
		2) Reflection in horizontal line first, then reflection in vertical line
		3) Combining two reflections r and r.  The Identity rigid motion denoted by I

	B) Team exercise: groups reflect a right triangle, first by a reflection in horizontal and then in a line at 45 degrees to the horizontal line:  what happened?

	C) Team exercise:  look at our 2 examples.  Can they see a pattern?
	
	D) Summary of where we are with rigid motions
		1) Reflection:  “fold”
		2) Rotation:  “turn”
		3) Translation:  “shift”
		4) Combining two rigid motions M and N
			a) Combining two reflections in intersecting lines yields a rotation
			b) Combining two reflections in parallel lines yields a translation
			c) Combining two reflections that are the same yields I, the Identity rigid motion

IV) Break

V) Tables for the composition of rigid motions

	A) How would we construct a composition table?

	B) Team exercise:  a rectangle
		1) Find all the reflections and rotations that send the rectangle back to the same rectangle
		2) Teams report on how many they found
		3) Teams construct the composition table for the rectangle
		4) Teams report 
		5) Color the rectangle so you lose the reflections.

	C) Team exercise:  an equilateral triangle
		1) Find all the reflections and rotations that send the triangle back to the same triangle
		2) Teams report on how many they found
		3) Teams construct the composition table for the triangle
		4) Teams report 
		5) Color the triangle so you lose the reflections.


	D) The formal names for the composition table
		1) The formal mathematical name for the table is a Group 
		2) The formal mathematical names for our examples
			a) Rectangle example:   D(2) and C(2) 
			b) triangle example:  D(3) and C(3)

VI) Homework
	
	A) Hand out assignment 6 due Monday April 17, 2006.

	B) Hand out assignment 7 due Wednesday April 19, 2006.

	C) Note: Get started early on this assignment.  It is much longer than earlier assignments and more challenging.