ENGLISH

The Mathematics of India: Concepts, Methods, Connections

By P. P. Divakaran

Book information

Publisher
Springer
Year
2018
ISBN
9789811317736, 9811317739
Language
english
Format
PDF
Filesize
4 MB (4524230 bytes)
Pages
441\441
Time added
2018-09-20 16:40:52

Description

This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry; a classical period inaugurated by Aryabhata’s invention of trigonometry and his enunciation of the principles of discrete calculus as applied to trigonometric functions; and a final phase that produced, in the work of Madhava, a rigorous infinitesimal calculus of such functions. The main highlight of this book is a detailed examination of these critical phases and their interconnectedness, primarily in mathematical terms but also in relation to their intellectual, cultural and historical contexts. Recent decades have seen a renewal of interest in this history, as manifested in the publication of an increasing number of critical editions and translations of texts, as well as in an informed analytic interpretation of their content by the scholarly community. The result has been the emergence of a more accurate and balanced view of the subject, and the book has attempted to take an account of these nascent insights. As part of an endeavour to promote the new awareness, a special attention has been given to the presentation of proofs of all significant propositions in modern terminology and notation, either directly transcribed from the original texts or by collecting together material from several texts. Front Matter ....Pages i-xxxiii Front Matter ....Pages 23-23 Background: Culture and Language (P. P. Divakaran)....Pages 25-42 Vedic Geometry (P. P. Divakaran)....Pages 43-71 Antecedents? Mathematics in the Indus Valley (P. P. Divakaran)....Pages 73-91 Decimal Numbers (P. P. Divakaran)....Pages 93-112 Numbers in the Vedic Literature (P. P. Divakaran)....Pages 113-140 Front Matter ....Pages 141-141 From 500 BCE to 500 CE (P. P. Divakaran)....Pages 143-173 The Mathematics of the Ganitapāda (P. P. Divakaran)....Pages 175-212 From Brahmagupta to Bhaskara II to Narayana (P. P. Divakaran)....Pages 213-254 Front Matter ....Pages 255-255 The Nila Phenomenon (P. P. Divakaran)....Pages 257-290 Nila Mathematics – General Survey (P. P. Divakaran)....Pages 291-311 The π Series (P. P. Divakaran)....Pages 313-329 The Sine and Cosine Series (P. P. Divakaran)....Pages 331-357 The π Series Revisited: Algebra in Analysis (P. P. Divakaran)....Pages 359-378 Front Matter ....Pages 379-379 What is Indian about the Mathematics of India? (P. P. Divakaran)....Pages 381-398 What is Indian . . .? The Question of Proofs (P. P. Divakaran)....Pages 399-412 Upasamhāra (P. P. Divakaran)....Pages 413-422 Back Matter ....Pages 423-441

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