Grade for hw4 for Chris Logie:

Problem 1.
(a)
    5 out of 5 points.
    Your arguments could have been tighter
    (e.g., if the weight of p_0 to p_7 are 3+epsilon more than the weight
    of p_8, then p_8 would have been redundant)  If is less than 3 more
    it would not be.
(b)
     4 out of 5 points.
     The argument is basically right, but somewhat incomplete.

     The basic lemma is this: if the vector p+r makes an angle
     GREATER than 90 degrees with the vector q-p, then for t>0
     sufficiently large,
     the weighted distance of p+tr from p would be greated
     than the weighted distance of p+tr from q.

	This is easily shown by an explicit computation involving
	trigonometry.
     
     If p is a vertex of the convex hull, and q is any other
     point in the convex hull, then we can choose a vector r
     with the property of the lemma.  QED

Problem 2.

(a) t(n) is Omega(n^2).  5 out of 5

(b) Does every tetrahedralization of S have Omega(n^2) tetras?
	Answer is NO.   0 out of 5.
	Your argument claims that every tetra must have 2 vertices
	from the z-axis.  But actually, we can have tetras with
	only 1 vertex from the z-axis and 3 from the circle.
	If you arrange this properly, you can get away with only
	O(n log n) tetras.

(c)