2024/05/18 by V. N. Krishnachandran, Krishnachandran, V. N.
Mathematics · #01A32 (Primary) #40-03 #40A05 (Secondary) #FOS: Mathematics #History and Overview (math.HO) #Mathematical Approximation and Integration #Mathematics and Applications #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2405.11144
openalex publication_date 2024/05/18 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28
This paper examines what computational procedures Śankara Varman (1774-1839) and Sangamagrama Mādhava (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 1017 by the former and a circle of diameter 9× 1011 by the latter). It is shown that if we choose the Mādhava-Gregory series for \tfracπ6=\arctan (\tfrac1√(3)) to compute π and then use it compute the circumference of a circle of diameter 1017 and perform the computations by ignoring the fractional parts in the results of every operation we get the value stated by Śankara Varman. It is also shown that, except in an unlikely case, none of the series representations of π attributed to Mādhava produce the value for the circumference attributed to him. The question how Mādhava did arrive at his value still remains unanswered.