Quote of the Day: 
     "Mathematics -- the subtle fine art."  -- Jamie Byrnie Shaw"

Objectives:
    The student will apply the delta-epsilon definition of a limit 
to making a Hexaflexagon.

1. Collect Homework.

2. Distribute sheets of adding machine paper to each student -- they 
	should be three feet in length.  
   Begin folding the sheets to form triangles – eventually they will 
   	become equilateral triangles.  Take the sheet and fold down 
	and make a crease.  Then unfold the paper and fold up along 
	the crease, making another crease.  Then unfold and fold down 
	along the last crease.  Continue this process until you have 
	25 triangles.  
   The last 19 triangles are the ones we will use – they should be 
	very close to equilateral!

3. The purpose of this exercise is to see that the angles in the 
	triangle are approaching 60 degrees.  Here is a proof (making 
	the triangles equilateral):

   Represent the first angle in triangle #1 by 60 + e degrees, where 
	e is the difference between the measure of the angle and 60 
	degrees.  Then using alternate interior angles, there is an 
	angle in triangle #2 which has this same measure.  Since the 
	sum of the angles along a line equal 180 degrees, and the 
	transversals represent the folds, the middle angle at the top 
	of triangle #2 must equal 60 – e/2 degrees.  Then continue 
	using alternate interior angles and the sum of the angles
	along a line equaling 180 degrees to discover the measures of 
	the remaining angles.  Notice that the angles are approaching 
	60 degrees:
	from (60+e) to (60-e/2) to (60+e/4) to (60-e/8) to (60+e/16), etc.
	If the original angle was 80 degrees, so that it was  off by 
	20 degrees (e = 20), then by triangle #5, e = 20/16 = 1.5 
	degrees!!!!  So the angle would equal 61.5 degrees.  And the 
	next ones would be closer.

5. Assignment: 
             Finish decorating all 6 sides of the Hexaflexagon
             p. 137 (6, 12, 30, 31)
             p. 145 (6, 16, 17)

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