id: 06426595
dt: j
an: 2015c.00015
au: Webb, Phoebe
ti: The development of calculus in the Kerala School.
so: Math. Enthus. 11, No. 3, 493-512 (2014).
py: 2014
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: A30 G60 I20 I30 N50
ut: 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
ci:
li: http://www.math.umt.edu/tmme/vol11no3/Webb_4.pdf
ab: 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
Madhavaâ€™s derivation of the power series for sine and cosine, as well
as a series similar to the well-known 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.
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