The mysterious and wonderfulis reduced to a gargle that helps computing machines clear their throats.
-- Philip J. DavisIn recent years, the computation of the expansion of
-- David H. BaileyIt requires a mere 39 digits of
(an upper bound on the distance travelled by a particle moving at the speed of light for 20 billion years, and as such an upper bound for the radius of the universe) with an error of less than
meters (a lower bound for the radius of a hydrogen atom).
-- Jonathan and Peter Borwein
has been the subject
of a great deal of mathematical (and popular) folklore. It's been worshipped, maligned,
and misunderstood. Overestimated, underestimated, and legislated. Of interest
to scholars, crackpots, and everyday people.
Pretty amazing accomplishments for a number!
The next few pages will attempt to teach you a few facts about
.
You will find here, among other things, a
brief history of extended precison approximations
of ,
including Archimedes' method
for estimating
,
a page full of
"oh, wow!" formulas
used to estimate
over the centuries, and a brief look at a
modern algorithm
used to compute
.
I also have a list of references for further reading
and a list of other pages devoted to pi on the Web.
Before we begin, it might not hurt to remind you that
is defined as the (constant) ratio of the circumference
to the diameter
in any circle.
In other words, the circumference and diameter of every circle are
known to be related by 
.
It's not hard to see (using only elementary geometry) that
is bigger than 3 but less than 4.
Neal Carothers - carother@bgnet.bgsu.edu