Summary – 10 Nov 2009 (prepared by David Henderson)
Chapter 13.
 It is OK to use algebra results such as: (a+b)2 = a2 + b2 +2ab but first show by picture that they
are true by dissection.
 In 13.4, if  /2 then the areas of the parallelograms formed are not equal to ac or bd -- what
is the area?
Chapter 20.
 In 20.1 use Figure 20.1 and relate the extrinsic radius r’ to the intrinsic radius r.
 In 20.2b, draw a triangle on a sphere with one angle and place the sphere on a piece of paper
so that this vertex is on the paper. Now project from the center of the sphere (gnomic projection).
O



Rc

b
a
C

G(B)
G(A)
To better see the details of this picture, we look separately at four triangles:
O
O
b*

a*
G(A)
b*
b
a
a*
S
a'
b'
G(B)
c
S
a'
G(A)

G(A)
b'
c'
Now use the planar Law of Cosines.
G(B)
c'
G(B)