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The mathematics of India : concepts, methods, connections

Author: P P Divakaran
Publisher: Singapore : Springer ; New Dehli : Hindustan Book Agency, [2018]. ©2018
Series: Sources and studies in the history of mathematics and physical sciences.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: History
Additional Physical Format: Online version:
Divakaran, P. P.
Mathematics of India.
Singapore : Springer, 2018
(OCoLC)1054128305
(DLC) 2018949905
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: P P Divakaran
ISBN: 9811317739 9789811317736
OCLC Number: 1042083302
Description: xi, 441 pages : illustrations ; 25 cm.
Contents: Preface --
Introduction --
Three Key Periods --
Sources --
Methodology --
Sanskrit and its Syllabary --
Beginnings --
Background : Culture and Language --
The Indus Valley Civilisation --
The Vedic Period --
The Oral Tradition --
Grammar --
Vedic Geometry --
The Śulbasūtra --
The Theorem of the Diagonal --
Rectilinear Figures and their Transformations --
Circle from Square : the Direct Construction --
The Inverse Formula : Square from Circle --
Antecedents? Mathematics in the Indus Valley --
Generalities --
Measures and Numbers --
Geometry --
Influences? --
Decimal Numbers --
Background --
Numbers and Based Numbers --
The Place-value Principle and its Realisations --
Other Realisations --
The Choice of a Base --
Numbers in the Vedic Literature --
Origins --
Number Names in the Rgveda --
Infinity and Zero --
Early Arithmetic --
Combinatorics --
The Aryabhatan Revolution --
From 500 BCE to 500 CE --
One Thousand Years of Invasions --
The Siddhantas and the Influence of Greek Astronomy --
Āryabhatị̄ya : An Overview --
Who was Aryabhata? --
The Bakhshali Manuscript : Where Does it Fit in? --
The Mathematics of the Ganịtapāda --
General Survey --
The Linear Diophantine Equation : kutṭạka --
The Invention of Trigonometry --
The Making of the Sine Table : Aryabhata's Rule --
Aryabhata's Legacy --
From Brahmagupta to Bhaskara II to Narayana --
Mathematics Moves South --
The Quadratic Diophantine Problem : bhāvanā --
Methods of Solution : cakravāla --
A Different Circle Geometry : Cyclic Quadrilaterals --
The Third Diagonal; Proofs --
Madhava and the Invention of Calculus --
The Nila Phenomenon --
The Nila School Rediscovered --
Mathematicians in their Villages : and in their Words --
The Sanskritisation of Kerala --
Who was Madhava? . . . and Narayana? --
Nila Mathematics : General Survey --
The Primary Source : Yuktibhāsạ̄ --
Geometry and Trigonometry; Addition Theorems --
The Sine Table; Interpolation --
Samṣkāram : Generating Infinite Series --
The ... Series --
Calculus and the Gregory-Leibniz Series --
The Geometry of Small Angles and their Tangents --
Integration : the Power Series --
Integrating Powers; Asymptotic Induction --
The Arctangent Series --
The Sine and Cosine Series --
From Differences to Differentials --
Solving the Difference, Differential Equation --
The Sphere --
The Calculus Debates --
The ... Series Revisited : Algebra in Analysis --
The Problem --
Polynomials : A Primer --
Higher Order Corrections --
Variations on the ... series --
Connections --
What is Indian about the Mathematics of India? --
The Geography of Indian Mathematics --
The Weight of the Oral Tradition --
Geometry with Indian Characteristics --
What is Indian . . .? The Question of Proofs --
What is a Proof? --
No Reductio ad Absurdum --
Recursion, Descent and Induction --
Upasamḥāra --
Towards Modernity --
Cross-cultural Currents? --
Journey's End --
Bibliography --
Index.
Series Title: Sources and studies in the history of mathematics and physical sciences.
Responsibility: P.P. Divakaran.

Abstract:

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  Read more...

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