 
Summary: 3rd
TEMPUSINTCOM Symposium, September 914, 2000, Veszprém, Hungary. 1
PI, FOURIER TRANSFORM AND LUDOLPH VAN CEULEN
M.Vajta
Department of Mathematical Sciences
University of Twente
P.O.Box 217, 7500 AE Enschede
The Netherlands
email: m.vajta@math.utwente.nl
ABSTRACT
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number
theory. Calculating more and more decimals of (first by hand and then from the mid20th
century, by
digital computers) not only fascinated mathematicians from ancient times but kept them busy as well. They
invented and applied hundreds of methods in the process but the known number of decimals remained only a
couple of hundred as of the late 19th
century. All that changed with the advent of the digital computers. And
although digital computers made possible to calculate thousands of decimals, the underlying methods hardly
changed and their convergence remained slow (linear). Until the 1970's. Then, in 1976, an innovative
quadratic convergent formula (based on the method of algebraicgeometric mean) for the calculation of
