Madhava (c. 1360-1420), an Empranitiri
living in India, created methods to compute accurate values for
functions by generating infinite series. His publications in
date to approximately 200 years before Maclaurin, Gregory, Wallis, et
Here is a literal translation of his verse:
Multiply the diameter (of the circle)
by 4 and
divide by 1. Then apply to this separately with negative and
signs alternately the product of the diameter and 4 divided by the odd
numbers 3, 5, and so on ...The result is the accurate circumference; it
is extremely accurate if the division is carried out many times.
This expression is equivalent to the
we usually attribute to Leibniz.