Department of Mathematics
Texas A & M - Commerce
Student/Faculty Colloquium
Friday, September 15, 2006
Binnion 329, 12:00pm (noon)
Rick Kreminski,
Texas A & M - Commerce math department,
will speak on:
How to compute π to (hundreds of) thousands of
digits from Vieta's venerable formula
Abstract:
Vieta's infinite product formula for π, using nested radicals of 2, has
been around for hundreds of years. Vieta himself
was able to deduce π to 8 digits past the decimal
using it in 1593. But surprisingly its convergence can
be dramatically accelerated, and this apparently has
not been known before. Perhaps this is simply because
it appears in the form of an infinite product, something
that is relatively rarely encountered.
We'll first show what Vieta's formula
is, and how it can be used to compute π to several
hundred thousand digits on a typical PC. The prerequisites
for this talk are the half-angle formulas from trigonometry,
and knowledge of the Taylor series for the sine function - that's
all.
All students and faculty are welcome to attend!