Calculus Transmission

Living reference work entry
DOI: https://doi.org/10.1007/978-94-007-3934-5_10326-1

It has gone unnoticed that Ᾱryabhaṭa’s 24 sine values (see “Calculus”) involved a striking departure from the earlier geometric tradition and a paradigm shift to numerical techniques. The geometric tradition is useful only in simple situations where high symmetry is present. It cannot be used to calculate the sine of 1° but was earlier used to compute 6 sine values 15° apart.

In a second radical departure, Ᾱryabhaṭa used difference equations, instead of algebraic equations. Indeed, in the tenth gītikā (this is called the tenth gītikā since the first two are invocations; Shukla & Sarma, 1976), of the daśgītikā section, he states only the sine differences:

Keywords

Infinite Series Solar Altitude Indian Text Gregorian Calendar Mass Translation 
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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.AlBukhary International UniversityAlor SetarMalaysia