Ancient Indian Leaps into Mathematics

This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian

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Ancient Indian Leaps into Mathematics

Editors B.S. Yadav (Deceased)

Man Mohan Ramjas College University of Delhi 110 007 New Delhi India [email protected]

ISBN 978-0-8176-4694-3 e-ISBN 978-0-8176-4695-0 DOI 10.1007/978-0-8176-4695-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010937771 Mathematics Subject Classification (2010): 01A32, 01A16, 01A17, 01A25, 01A27, 01A29 c Springer Science+Business Media, LLC 2011  All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper www.birkhauser-science.com

Dedicated to the memory of U. N. SINGH The Founder of the Indian Society for History of Mathematics

U. N. Singh (November 19, 1920 – April 9, 1989)

Professor B. S. Yadav (31 July 1931 – 24 February 2010) B. S. Yadav was born in Mathura, India. He dedicated his whole life to the cause of mathematics and the history of mathematical sciences. After obtaining his B Sc (1953) and M Sc (1957) degrees from Agra University and Aligarh Muslim University, respectively, he pursued research in mathematics at M. S. University, Baroda, for which he was awarded the Ph.D. in 1965. Through his extended research career he made significant contributions to functional analysis, operator theory, Fourier analysis, and studies in the history of mathematics. His teaching career started at M. S. University, Baroda (Lecturer, 1956–1964). He then moved to Sardar Patel University, Vallabh Vidya Nagar, Gujarat (Reader, 1964–1970), and later to Delhi University (Reader, 1970–1976 & Professor, 1976–1996). He played an influential role at various universities and Indian boards of studies. Besides serving on numerous important committees such as the Academic Council and Research Degree Committee, he also worked as Head of the Department of Mathematics and as Dean of the Faculty of Mathematical Sciences in Delhi University for several years. He was widely traveled, with over 25 visits to various universities abroad, and was a Visiting Professor of Mathematics at Cleveland State University, Cleveland, Ohio, USA during 1987–1988. He was associated with several academic bodies and research journals. He was a founding member of the Indian Society for History of Mathematics, founded by his guide and mentor, the late Professor Udita Narayana Singh in 1978. He was deeply and emotionally involved with this society and was the mai