Archimedes's Theorems about pi

   The Ancient Greeks knew of at least four constants related to
circles and spheres, such as the ratio of the circumference to the
diameter of a circle, or the ratio of the volume of a sphere to a
cube inscribing it.  What they did not know, but may have
suspected, is that these constants are all essentially the same
(maybe after multiplying by some rational number like 1/6).  The
essential equality of these four constants was discovered and
proven by Archimedes, perhaps the greatest mathematician of
antiquity.  On this pi day in 2019, I will explain this and more,
and give you an idea of his amazing proofs.