Pi is one of the few concepts in
mathematics whose mention evokes a response of recognition and
interest in those not concerned professionally with the subject.
It has been a part of human culture and the educated imagination
for more than twenty five hundred years.
The computation of Pi is virtually
the only topic from the most ancient stratum of mathematics that
is still of serious interest to modern mathematical research. And
to pursue this topic as it developed throughout the millennia is
to follow a thread through the history of mathematics that winds
through geometry, analysis and special functions, numerical
analysis, algebra and number theory. It offers a subject which
provides mathematicians with examples of many current mathematical
techniques as well as a palpable sense of their historical
development."
The above passage is taken from the introduction
to "Pi : A Source Book" by L. Berggren, J. Borwein and P. Borwein. It is a
large collection of papers on pi and will appear with Springer-Verlag sometime
in 1997. Much additional material is available in the 1986 Wiley volume "Pi and the AGM" by J. Borwein and P. Borwein.