A Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact
Publication Year: 2009
This book traces the first faltering steps taken in the mathematical theorization of infinity which marks the emergence of modern mathematics. It analyzes the part played by Indian mathematics through the Kerala conduit, which is an important but neglected part of the history of mathematics.
- Front Matter
- Back Matter
- Subject Index
- Chapter 1: Introduction
- Chapter 2: The Social Origins of the Kerala School
- Chapter 3: The Mathematical Origins of the Kerala School
- Chapter 4: The Highlights of Kerala Mathematics and Astronomy
- Chapter 5: Indian Trigonometry: From Ancient Beginnings to Nilakantha
- Chapter 6: Squaring the Circle: The Kerala Answer
- Chapter 7: Reaching for the Stars: The Power Series for Sines and Cosines
- Chapter 8: Changing Perspectives on Indian Mathematics
- Chapter 9: Exploring Transmissions: A Case Study of Kerala Mathematics
- Chapter 10: A Final Assessment
Copyright © George Gheverghese Joseph, 2009
All rights reserved. No part of this book may be reproduced or utilised in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage or retrieval system, without permission in writing from the publisher.
First published in 2009 by
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Library of Congress Cataloging-in-Publication Data
Joseph, George Gheverghese.
A passage to infinity: medieval Indian mathematics from Kerala and its impact/George Gheverghese Joseph.
Includes bibliographical references and index.
1. Mathematics—India—Kerala—History. 2. Mathematics, Medieval. 3. Astronomy, Medieval—India—Kerala. I. Title.
QA27.I4J67 510.954′830902—dc22 2009 2009035222
ISBN: 978-81-321-0168-0 (HB)
The SAGE Team: Rekha Natarajan, Sushmita Banerjee and Trinankur Banerjee
This book is dedicated to my six grandchildren, Sonya, Maya, Tabitha, Zinzi, Petra and Milo, who are encouraged to read whatever appeals to their minds and imaginations, think thoughts that uplift and always have a corner in their hearts for their Indian heritage.[Page vi]
List of Tables and Figures[Page viii]Tables
- 2.1 Major Personalities and Texts (in Italics) in Indian Mathematics 12
- 3.A.1 Applying Bhaskara I's Approximation Formula in Degrees 58
- 3.A.2 Applying Bhaskara II's Approximation Formula in Radians 62
- 5.1 Aryabhata's Sine Table 89
- 5.2 Varahamihira's Table of Sine-Differences 91
- 5.3 Brahmagupta's Table of Sines 94
- 2.1 The Madhava (or Kerala) School of Indian Mathematics 16
- 3.1 The Rat and Hawk: An Application of the Pythagorean Theorem 47
- 4.1 Area = ½ Circumference × ½ Diameter 69
- 4.2 The Chord of a Circle 70
- 4.3 Summation of Arithmetical Series 72
- 4.4 Circum-radius of a Cyclical Quadrilateral 74
- 5.1 The Length of a Chord 83
- 5.2 Basic Concepts in Indian Trigonometry 84
- 5.3 A Geometric Evaluation of RSines 99
- 6.1 Summation of a Geometric Series: Visual Demonstration 115 [Page ix]
- 6.2 Summation of Geometric Series: A Geometric Demonstration 116
- 6.3 Area under a Curve 118
- 6.4 A Tangent to a Circle 119
- 6.5 Derivation of the Madhava—Gregory Series 120
- 6.6 Steps in the Derivation of the Madhava—Gregory Series Derivation. 122
- 7.1 The Derivation of Sine and Cosine 147
- 7.2 The Derivation of Sine and Cosine Series 149
- 8.1 Early Indian Numerals 167
- 8.2 Indian Numerals around the 11th Century 168
Like any book, this could not have been written without the help of many people. However, a special acknowledgement should be made for those who were members of the Arts and Humanities Research Board (AHRB) Research Project on Medieval Kerala Mathematics. In particular, I would like to acknowledge the help of Dr V. Madhukar Mallayya who was the Research Associate and whose expertise and insights were crucial to the successful outcome of the project, especially the comprehensive survey that he carried out for the project entitled ‘Trigonometric Sines and Sine Tables in India’ (unpublished). This was an important source for Chapter 5 of this book. I would also like to acknowledge the valuable inputs of Mr Dennis Almeida (Member of the research team), Dr M. Vijayalekshmy (Research Assistant), Dr J.M. DeLire (Research Assistant) and Dr C. Goncalves (Research Assistant). Their specific contributions are referred to in various parts of this book.
Note: No mathematical significance should be drawn from the use of lower case and upper case first letters (for example, Sine [sine] or Cosine [cosine]) throughout the book unless specifically pointed out.[Page xii]
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About the Author[Page 220]
George Gheverghese Joseph was born in Kerala, India. His family moved to Mombasa in Kenya where he did his schooling. He studied at the University of Leicester, the United Kingdom, and then worked for six years in Kenya before pursuing his postgraduate studies at Manchester, the United Kingdom. He has travelled widely, holding university appointments and giving lectures at various universities around the world. He has appeared on radio and television programmes in India, the United States, Australia, South Africa and New Zealand, as well as the United Kingdom. In January 2000, he helped to organise an International Seminar and Colloquium to commemorate the 1500th year of Aryabhata's famous text, Aryabhateeyam; the seminar was held in Thiruvanthapuram, Kerala. In December 2005, he organised an International Workshop at Kovalam which was the culmination of a AHRB-funded Research Project on ‘Medieval Kerala Mathematics: The Possibility of Its Transmission to Europe’. In 2008, he gave talks at Loyola University, Chicago, USA and the Mathematical Association of America (MAA), reporting on the findings of the AHRB project. He holds joint appointments at the University of Manchester and at the University of Toronto, Canada.
He authored the bestseller The Crest of the Peacock: Non-European Roots of Mathematics (1991). His other works include George Joseph: The Life and Times of a Kerala Christian Nationalist (2003), Multicultural Mathematics (1993) and Women at Work: The British Experience (1983).