In article <ken.pledger-1BCED6.firstname.lastname@example.org> Ken Pledger <email@example.com> writes: > In article > <firstname.lastname@example.org>, > calvin <email@example.com> wrote: > > I've often wondered how the ancients were able to > > find the value of pi so precisely as to know that > > it is not rational.... > > AFAIK they didn't. The irrationals in Euclid Book X are all > algebraic numbers built up from square roots.
They did not know that pi is irrational. The first proof dates from the 18th century. A short proof (requiring not much more than calculus, but more than the Greek knew about) was found in 1947. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/