
06426595
j
2015c.00015
Webb, Phoebe
The development of calculus in the Kerala School.
Math. Enthus. 11, No. 3, 493512 (2014).
2014
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
A30
G60
I20
I30
N50
history of mathematics
Indian mathematics
calculus
power series for sine and cosine
trigonometric series
Kerala School
Madhava
trigonometry
mathematical culture in India
mathematical culture in Europe
Greek mathematics
sine function
reversed sine
sums
circles
arcs
chords
sum of powers of integers
infinite series
Taylor series
approximation
cosine
approximations of trigonometric functions
http://www.math.umt.edu/tmme/vol11no3/Webb_4.pdf
Summary: The Kerala School of mathematics, founded by Madhava in Southern India, produced many great works in the area of trigonometry during the fifteenth through eighteenth centuries. This paper focuses on Madhava's derivation of the power series for sine and cosine, as well as a series similar to the wellknown Taylor series. The derivations use many calculus related concepts such as summation, rate of change, and interpolation, which suggests that Indian mathematicians had a solid understanding of the basics of calculus long before it was developed in Europe. Other evidence from Indian mathematics up to this point such as interest in infinite series and the use of a base ten decimal system also suggest that it was possible for calculus to have developed in India almost 300 years before its recognized birth in Europe. The issue of whether or not Indian calculus was transported to Europe and influenced European mathematics is not addressed.