Spoken Text and Written Symbol: The Use of Layout and Notation in Sanskrit Scientific Manuscripts

Because of the traditional reverence for oral composition and recitation in Sanskrit literature, most Classical Sanskrit treatises, including scientific ones, were composed in verse and intended (at least in theory) for memorization. Written versions of Sanskrit texts are often presented in imitation of their ideal oral form, as an almost continuous and unformatted stream of syllables. Manuscripts of technical works on subjects such as mathematics and astronomy, however, had to combine this “one-dimensional” text stream with graphical and notational features generally requiring two-dimensional layout, such as tables, diagrams, and equations. This paper looks at how the ways in which this synthesis could be achieved posed several significant challenges for Sanskrit scribes

An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text

AbstractMathematical approximation by iterative algorithms is well attested in Sanskrit astronomical texts, but its use has not been studied systematically. In his 14th-century supercommentary on Govindasvāmin's commentary on Bhāskara I'sMahābhāskarı̄ya, Parameśvara, a student of the renowned Kerala astronomer Mādhava, presents a one-point iterative technique for calculating the Sine of a given angle, as well as a modification of this technique that involves a two-point algorithm essentially identical to the modern secant method. This paper presents a mathematical and historical interpretation of his remarks.L'approximation mathématique par les procédés d'itération se manifeste fréquemment dans les textes sanscrites astronomiques, mais elle n'est pas beaucoup étudiée. Dans son surcommentaire sur le commentaire de Govindasvāmin sur leMahābhāskarı̄yade Bhāskara I, Parameśvara, un élève de Mādhava, l'astronome renommé de Kerala, donne un calcul itératif en virgule fixe pour le calcul du Sinus d'un angle donné, aussi bien qu'une modification de cette méthode dans laquelle paraı̂t une technique virtuellement identique à la forme discrète de la méthode de Newton–Raphson. L'article suivant présente une interpretation mathématique et historique de ses rémarques.Die mathematische Annäherung bei den Iterationsverfahren ist in den sanskritischen astronomischen Texten gut bezeugt, aber darüber gibt es nicht viele Studien. In seiner Kommentar über Govindasvāmins Kommentar über dieMahābhāskarı̄yades ersten Bhāskaras gibt, Parameśvara, ein Student des bekannten keralischen Astronomen Mādhavas, eine Festkommarechnung für die Berechnung des Sinus eines gegebenen Winkels, wie auch eine Modifikation dieser Technik; diese Modifikation enthält einen Algorithmus der grundsätzlich der diskreten Newton–Raphsonischen Methode gleichwertig ist. Dieser Artikel stellt eine mathematische und historische Interpretation seiner Bemerkungen dar

Mathematics in India

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic s