The mathematics of India : concepts, methods, connections / P. P. Divakaran.
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...
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| Format: | eBook |
| Language: | English |
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Singapore :
Springer,
2018.
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| Series: | Sources and studies in the history of mathematics and physical sciences.
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| Subjects: |
MARC
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| 100 | 1 | |a Divakaran, P. P., |e author. |0 http://id.loc.gov/authorities/names/n90670991 |1 http://isni.org/isni/0000000029324296. | |
| 245 | 1 | 4 | |a The mathematics of India : |b concepts, methods, connections / |c P. P. Divakaran. |
| 264 | 1 | |a Singapore : |b Springer, |c 2018. | |
| 300 | |a 1 online resource (xi, 441 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
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| 490 | 1 | |a Sources and studies in the history of mathematics and physical sciences, |x 2196-8810. | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Intro; Preface; Contents; Introduction; 0.1 Three Key Periods; 0.2 Sources; 0.3 Methodology; 0.4 Sanskrit and its Syllabary; Part I: Beginnings; 1: Background: Culture and Language; 1.1 The Indus Valley Civilisation; 1.2 The Vedic Period; 1.3 The Oral Tradition; 1.4 Grammar; 2: Vedic Geometry; 2.1 The Śulbasūtra; 2.2 The Theorem of the Diagonal; 2.3 Rectilinear Figures and their Transformations; 2.4 Circle from Square: The Direct Construction; 2.5 The Inverse Formula: Square from Circle; 3: Antecedents? Mathematics in the Indus Valley; 3.1 Generalities; 3.2 Measures and Numbers; 3.3 Geometry. | |
| 505 | 8 | |a 3.4 Influences?4: Decimal Numbers; 4.1 Background; 4.2 Numbers and Based Numbers; 4.3 The Place-value Principle and its Realisations; 4.4 Other Realisations; 4.5 The Choice of a Base; 5: Numbers in the Vedic Literature; 5.1 Origins; 5.2 Number Names in the Rgveda; 5.3 Infinity and Zero; 5.4 Early Arithmetic; 5.5 Combinatorics; Part II: The Aryabhatan Revolution; 6: From 500 BCE to 500 CE; 6.1 One Thousand Years of Invasions; 6.2 The Siddhantas and the Influence of Greek Astronomy; 6.3 Āryabhatīya -- An Overview; 6.4 Who was Aryabhata?; 6.5 The Bakhshali Manuscript: Where Does it Fit in? | |
| 505 | 8 | |a 7: The Mathematics of the Ganitapāda7.1 General Survey; 7.2 The Linear Diophantine Equation -- kuttaka; 7.3 The Invention of Trigonometry; 7.4 The Making of the Sine Table: Aryabhata's Rule; 7.5 Aryabhata's Legacy; 8: From Brahmagupta to Bhaskara II to Narayana; 8.1 Mathematics Moves South; 8.2 The Quadratic Diophantine Problem -- bhāvanā; 8.3 Methods of Solution -- cakravāla; 8.4 A Different Circle Geometry: Cyclic Quadrilaterals; 8.5 The Third Diagonal; Proofs; Part III: Madhava and the Invention of Calculus; 9: The Nila Phenomenon; 9.1 The Nila School Rediscovered. | |
| 520 | |a 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.-- |c Provided by publisher. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed September 25, 2018) | |
| 650 | 0 | |a Mathematics |z India |x History. |0 http://id.loc.gov/authorities/subjects/sh2010101033. | |
| 776 | 0 | 8 | |c Original |z 9811317739 |z 9789811317736 |w (OCoLC)1042083302. |
| 830 | 0 | |a Sources and studies in the history of mathematics and physical sciences. |0 http://id.loc.gov/authorities/names/n99050535. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-13-1774-3 |z Full Text (via Springer) |
| 880 | 8 | |6 505-00 |a 9.2 Mathematicians in their Villages - and in their Words9.3 The Sanskritisation of Kerala; 9.4 Who was Madhava. . . and Narayana; 10: Nila Mathematics - General Survey; 10.1 The Primary Source: Yuktibhāsā; 10.2 Geometry and Trigonometry; Addition Theorems; 10.3 The Sine Table; Interpolation; 10.4 Samskāram: Generating Infinite Series; 11: The π Series; 11.1 Calculus and the Gregory-Leibniz Series; 11.2 The Geometry of Small Angles and their Tangents; 11.3 Integration: The Power Series; 11.4 Integrating Powers; Asymptotic Induction; 11.5 The Arctangent Series. | |
| 880 | 8 | |6 505-00 |a 12: The Sine and Cosine Series12.1 From Differences to Differentials; 12.2 Solving the Difference/Differential Equation; 12.3 The Sphere; 12.4 The Calculus Debates; 13: The π Series Revisited: Algebra in Analysis; 13.1 The Problem; 13.2 Polynomials: A Primer; 13.3 Higher Order Corrections; 13.4 Variations on the π series; Part IV: Connections; 14: What is Indian about the Mathematics of India; 14.1 The Geography of Indian Mathematics; 14.2 The Weight of the Oral Tradition; 14.3 Geometry with Indian Characteristics; 15: What is Indian . . .The Question of Proofs; 15.1 What is a Proof. | |
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