The Three Ages of Pi

The Age of Archimedean Polygons

Archimedes' proof that Pi is the area of a unit circle

-- and his method as a modern iteration.

The Age of Newtonian Calculus

Newton in Maple

from Gregory, Leibniz and Machin
-- to Shanks and ENIAC.

ENIAC, developed during the war, computed Pi (Euler's 1737 notation) to 2037 places in 1949.

The Age of Elliptic Functions

and the
Arithmetic Geometric Mean Iteration
of Gauss and Legendre.

Ramanujan in Maple

and Related Record Setting Quartic Algorithm in Maple

The Stamp honouring the 75th Anniversary of Ramanujan's birth - mailed to my father.

SFU/CECM/~jborwein/. Last revised 25/10/99 JMB