ABSTRACT
Mathematical proofs, like diamonds, are hard as well as clear, and w i l l be touched wi th nothing but strict reasoning.
John Locke, 1690, from Wi l l i am Dunham, The Mathematical Universe
As we noted i n [43], a computa t iona l or constructive approach can often
make a proof significantly more understandable. W h a t ' s more, the key con-
cepts involved are made more apparent, and are more l ikely to be remem-
bered later. Here we present some addi t iona l examples of computer-aided
proofs, inc lud ing some examples of "var ia t ional" methods of proof.
