  This paper examines what computational procedures \'Sankara Varman
(1774-1839) and Sangamagrama M\=adhava (c. 1340 - 1425),
astronomer-mathematicians of the Kerala school, might have used to arrive at
their respective values for the circumferences of certain special circles (a
circle of diameter $10^{17}$ by the former and a circle of diameter $9\times
10^{11}$ by the latter). It is shown that if we choose the M\=adhava-Gregory
series for $\tfrac{\pi}{6}=\arctan (\tfrac{1}{\sqrt{3}})$ to compute $\pi$ and
then use it compute the circumference of a circle of diameter $10^{17}$ and
perform the computations by ignoring the fractional parts in the results of
every operation we get the value stated by \'Sankara Varman. It is also shown
that, except in an unlikely case, none of the series representations of $\pi$
attributed to M\=adhava produce the value for the circumference attributed to
him. The question how M\=adhava did arrive at his value still remains
unanswered.
