He can also trisect an angle -- all it takes is infinite iterations.
As iterations -> infinity, then angle -> trisection.
A nice application of the theory of limits and a solution to one of Euclid's three unsolvable problems.
I figured out the essence of it in eighth grade. Having just read, again, that it isn't possible, I thought I'd say something.
Otherwise, I did enjoy Why Beauty Is Truth: A History of Symmetry.