[net.math] Banach-Tarski

mac (12/15/82)

There's a nice exposition of the Banach-Tarski theorem in the March 79
_____________________________American Mathematical Monthly.

It mentions a construction cutting a sphere into 5 pieces, and
reassembling them into two spheres, each congruent to the first.  This
should not be taken to mean that "a billiard ball can be chopped into
pieces which can then be put back together to form a life-size statue
of Banach".  One of the pieces above is a single point.  Nonetheless,
it shows what the Axiom of Choice can do in the right hands.  They
don't call it the Axiom "of Choice" for nothing.