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Table of Contents
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
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?
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
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?
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