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1. Essent Vol. 1
ESSENT Society for Collaborative Research and Innovation, IIT Mandi Editor: Athar Aamir Khan Editorial Support: Hemant Jalota Tejas Lunawat Advisory Committee: Dr Venkata Krishnan, Indian Institute of Technology Mandi Dr Varun Dutt, Indian Institute of Technology Mandi Dr Manu V. Devadevan, Indian Institute of Technology Mandi Dr Suman, Indian Institute of Technology Mandi AcknowledgementAcknowledgements: Prof. Arghya Taraphdar, Indian Institute of Technology Kharagpur Dr Shail Shankar, Indian Institute of Technology Mandi Dr Rajeshwari Dutt, Indian Institute of Technology Mandi SCRI Support teamteam:::: Abhishek Kumar, Nagarjun Narayan, Avinash K. Chaudhary, Ankit Verma, Sourabh Singh, Chinmay Krishna, Chandan Satyarthi, Rajat Raj, Hrudaya Rn. Sahoo, Sarvesh K. Gupta, Gautam Vij, Devang Bacharwar, Sehaj Duggal, Gaurav Panwar, Sandesh K. Singh, Himanshu Ranjan, Swarna Latha, Kajal Meena, Shreya Tangri. ©SOCIETY FOR COLLABORATIVE RESEARCH AND INNOVATION (SCRI), IIT MANDI [email protected] Published in April 2013 Disclaimer: The views expressed in ESSENT belong to the authors and not to the Editorial board or the publishers. The publication of these views does not constitute endorsement by the magazine. The editorial board of ‘ESSENT’ does not represent or warrant that the information contained herein is in every respect accurate or complete and in no case are they responsible for any errors or omissions or for the results obtained from the use of such material. Readers are strongly advised to confirm the information contained herein with other dependable sources. ESSENT|Issue1|V ol1 ESSENT Society for Collaborative Research and Innovation, IIT Mandi CONTENTS Editorial 333 Innovation for a Better India Timothy A. Gonsalves, Director, Indian Institute of Technology Mandi 555 Research, Innovation and IIT Mandi 111111 Subrata Ray, School of Engineering, Indian Institute of Technology Mandi INTERVIEW with Nobel laureate, Professor Richard R. -
Kamala¯Kara Commentary on the Work, Called Tattvavivekodāharan
K related to the Siddhānta-Tattvaviveka, one a regular Kamala¯kara commentary on the work, called Tattvavivekodāharan. a, and the other a supplement to that work, called Śes.āvasanā, in which he supplied elucidations and new K. V. SARMA material for a proper understanding of his main work. He held the Sūryasiddhānta in great esteem and also wrote a Kamalākara was one of the most erudite and forward- commentary on that work. looking Indian astronomers who flourished in Varanasi Kamalākara was a critic of Bhāskara and his during the seventeenth century. Belonging to Mahar- Siddhāntaśiroman. i, and an arch-rival of Munīśvara, a ashtrian stock, and born in about 1610, Kamalākara close follower of Bhāskara. This rivalry erupted into came from a long unbroken line of astronomers, bitter critiques on the astronomical front. Thus Ranga- originally settled at the village of Godā on the northern nātha, younger brother of Kamalākara, wrote, at the . banks of the river Godāvarī. Towards AD 1500, the insistence of the latter, a critique on Munīśvara’s Bhangī family migrated to Varanasi and came to be regarded as method (winding method) of true planets, entitled . reputed astronomers and astrologers. Kamalākara Bhangī-vibhangī (Defacement of the Bhangi), to which . studied traditional Hindu astronomy under his elder Munīśvara replied with a Khand.ana (Counter). Munīś- brother Divākara, but extended the range of his studies vara attacked the theory of precession advocated by to Islamic astronomy, particularly to the school of Kamalākara, and Ranganātha refuted the criticisms of his Ulugh Beg of Samarkand. He also studied Greek brother in his Loha-gola-khan. -
Mathematics Newsletter Volume 21. No4, March 2012
MATHEMATICS NEWSLETTER EDITORIAL BOARD S. Ponnusamy (Chief Editor) Department of Mathematics Indian Institute of Technology Madras Chennai - 600 036, Tamilnadu, India Phone : +91-44-2257 4615 (office) +91-44-2257 6615, 2257 0298 (home) [email protected] http://mat.iitm.ac.in/home/samy/public_html/index.html S. D. Adhikari G. K. Srinivasan Harish-Chandra Research Institute Department of Mathematics, (Former Mehta Research Institute ) Indian Institute of Technology Chhatnag Road, Jhusi Bombay Allahabad 211 019, India Powai, Mumbai 400076, India [email protected] [email protected] C. S. Aravinda B. Sury, TIFR Centre for Applicable Mathematics Stat-Math Unit, Sharadanagar, Indian Statistical Institute, Chikkabommasandra 8th Mile Mysore Road, Post Bag No. 6503 Bangalore 560059, India. Bangalore - 560 065 [email protected], [email protected] [email protected] M. Krishna G. P. Youvaraj The Institute of Mathematical Sciences Ramanujan Institute CIT Campus, Taramani for Advanced Study in Mathematics Chennai-600 113, India University of Madras, Chepauk, [email protected] Chennai-600 005, India [email protected] Stefan Banach (1892–1945) R. Anantharaman SUNY/College, Old Westbury, NY 11568 E-mail: rajan−[email protected] To the memory of Jong P. Lee Abstract. Stefan Banach ranks quite high among the founders and developers of Functional Analysis. We give a brief summary of his life, work and methods. Introduction (equivalent of middle/high school) there. Even as a student Stefan revealed his talent in mathematics. He passed the high Stefan Banach and his school in Poland were (among) the school in 1910 but not with high honors [M]. -
Chapter Two Astrological Works in Sanskrit
51 CHAPTER TWO ASTROLOGICAL WORKS IN SANSKRIT Astrology can be defined as the 'philosophy of discovery' which analyzing past impulses and future actions of both individuals and communities in the light of planetary configurations. Astrology explains life's reaction to planetary movements. In Sanskrit it is called hora sastra the science of time-'^rwRH ^5R5fai«fH5iref ^ ^Tm ^ ^ % ^i^J' 11 L.R. Chawdhary documented the use of astrology as "astrology is important to male or female as is the case of psychology, this branch of knowledge deals with the human soul deriving awareness of the mind from the careful examination of the facts of consciousness. Astrology complements everything in psychology because it explains the facts of planetary influences on the conscious and subconscious providing a guideline towards all aspects of life, harmony of mind, body and spirit. This is the real use of astrology^. Dr. ^.V.Raman implies that "astrology in India is a part of the whole of Indian culture and plays an integral part in guiding life for all at all stages of life" ^. Predictive astrology is a part of astronomy that exists by the influence of ganita and astronomical doctrines. Winternitz observes that an astrologer is required to possess all possible noble quantities and a comprehensive knowledge of astronomy, ' Quoted from Sabdakalpadruma, kanta-ll, p.550 ^ L.R.Chawdhari, Secrets of astrology. Sterling Paper backs, New Delhi,1998, p.3 ^Raman.B.V, Planetary influence of Human affairs, U.B.S. Publishers, New Delhi, 1996,p.147 52 mathematics and astrology^ Astrology or predictive astrology is said to be coconnected with 'astronomy'. -
History of Science and Technology in India
DDCE/History (M.A)/SLM/Paper HISTORY OF SCIENCE AND TECHNOLOGY IN INDIA By Dr. Binod Bihari Satpathy 1 CONTENT HISTORY OF SCIENCE AND TECHNOLOGY IN INDIA Unit.No. Chapter Name Page No Unit-I. Science and Technology- The Beginning 1. Development in different branches of Science in Ancient India: 03-28 Astronomy, Mathematics, Engineering and Medicine. 2. Developments in metallurgy: Use of Copper, Bronze and Iron in 29-35 Ancient India. 3. Development of Geography: Geography in Ancient Indian Literature. 36-44 Unit-II Developments in Science and Technology in Medieval India 1. Scientific and Technological Developments in Medieval India; 45-52 Influence of the Islamic world and Europe; The role of maktabs, madrasas and karkhanas set up. 2. Developments in the fields of Mathematics, Chemistry, Astronomy 53-67 and Medicine. 3. Innovations in the field of agriculture - new crops introduced new 68-80 techniques of irrigation etc. Unit-III. Developments in Science and Technology in Colonial India 1. Early European Scientists in Colonial India- Surveyors, Botanists, 81-104 Doctors, under the Company‘s Service. 2. Indian Response to new Scientific Knowledge, Science and 105-116 Technology in Modern India: 3. Development of research organizations like CSIR and DRDO; 117-141 Establishment of Atomic Energy Commission; Launching of the space satellites. Unit-IV. Prominent scientist of India since beginning and their achievement 1. Mathematics and Astronomy: Baudhayan, Aryabhtatta, Brahmgupta, 142-158 Bhaskaracharya, Varahamihira, Nagarjuna. 2. Medical Science of Ancient India (Ayurveda & Yoga): Susruta, 159-173 Charak, Yoga & Patanjali. 3. Scientists of Modern India: Srinivas Ramanujan, C.V. Raman, 174-187 Jagdish Chandra Bose, Homi Jehangir Bhabha and Dr. -
Kerala School of Astronomy and Mathematics
Kerala School of Astronomy and Mathematics M. D. Srinivas Centre for Policy Studies, Chennai E-mail: [email protected] In the first quarter of the nineteenth century, Benjamin Heyne According to some scholars, the great Aryabhata hailed and Charles Whish, officers serving under the East India from Kerala, though he wrote his treatise Aryabhatiya at Company, came across traditional practitioners of Indian Kusumapura or modern Patna in 499 CE. Kerala is of course astronomy who seemed to be conversant with several infinite known for many important astronomers such as Haridatta series for the ratio of the circumference to the diameter of (c.650–700) the originator of the well-known Parahita system a circle (denoted by the Greek symbol π in modern mathe- (founded at Tirunavay in 683), Govindasvamin (c.800), matics) and for the trigonometric functions sine and cosine. Sankaranarayana (c.825–900) and Udayadivakara (c.1073), Such series were generally believed to have been discovered but it was Madhava (c.1340–1425) of Sangama Grama (near first in Europe by Gregory, Newton and Leibniz in the second present-day Ernakulam) who was the pioneer of a new School. half of the 17th century. The later members of the school, starting from Madhava’s Heyne’s observations were recorded in the work disciple Paramesvara (c.1380–1460), lived mostly around the Kalasankalita published in 1825 CE by John Warren of the river Nila or Bharatapuzha in South Malabar. Madras Observatory. Charles Whish read a paper before the After Madhava, the next important member of the school Madras Literary Society in 1832, which was subsequently was Nilakantha Somasutvan (c.1444–1550) of Trikantiyur, published in the Transactions of the Royal Asiatic Society, who was the disciple of Damodara, the son of Paramesvara. -
Joseph G.G. a Passage to Infinity.. Medieval Indian Mathematics From
A Passage to Infi nity A Passage to Infi nity Medieval Indian Mathematics from Kerala and Its Impact GEORGE GHEVERGHESE JOSEPH 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 photocopy- ing, recording or by any information storage or retrieval system, without permission in writing from the publisher. First published in 2009 by SAGE Publications India Pvt Ltd B1/I-1 Mohan Cooperative Industrial Area Mathura Road, New Delhi 110 044, India www.sagepub.in SAGE Publications Inc 2455 Teller Road Thousand Oaks California 91320, USA SAGE Publications Ltd 1 Oliver’s Yard 55 City Road London EC1Y 1SP, United Kingdom SAGE Publications Asia-Pacifi c Pte Ltd 33 Pekin Street #02-01 Far East Square Singapore 048763 Published by Vivek Mehra for SAGE Publications India Pvt Ltd, Photo- typeset in 10.5/12.5 AGaramond by Tantla Composition Services Private Limited, Chandigarh and printed at Chaman Enterprises, New Delhi. Library of Congress Cataloging-in-Publication Data Joseph, George Gheverghese. A passage to infi nity: medieval Indian mathematics from Kerala and its impact/George Gheverghese Joseph. p. cm. Includes bibliographical references and index. 1. Mathematics—India—Kerala—History. 2. Mathematics, Medieval. 3. Astronomy, Medieval—India—Kerala. I. Title. QA27.I4J67 510.954Ј830902—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. -
Kerala School of Astronomy and Mathematics
We recall that in a magic square, the numbers in the rows, 114118 columns and diagonals sum to the same magic total. In a 12 7 2 13 pan-diagonal magic square, the broken diagonals also yield 6 9 16 3 the same magic total. Succinctly put, pan-diagonal magic 15 4 5 10 squares have the remarkable property that they can be con- This turns out to be one of the 384 magic squares considered by sidered as a magic squares “on the torus”. It is of interest Narayana Pandita. (Notice that rows, columns, diagonals and to note that Rosser and Walker proved in 1936 (the proof broken diagonals add to 34. For example, 5 + 3 + 12 + 14 = was simplified by Vijayaraghavan in 1941) that there are 12 + 9 + 5 + 8 = 34). only 384 pan-diagonal 4 × 4 magic squares with entries Xenophanes, the founder of the Eleatic School of Philo- 1, 2,...,16. sophy, had the well known dictum – Ex nihilo nihil fit, “Out Curiously enough, Ramanujan, in his notebooks of nothing, nothing comes”. One wonders whether after all of probably his earliest school days, has the magic Ramanujan was indeed influenced somewhat by the mathe- square matical tradition of his ancestors. Kerala School of Astronomy and Mathematics M. D. Srinivas Centre for Policy Studies, Chennai E-mail: [email protected] In the first quarter of the nineteenth century, Benjamin Heyne and mathematics, at least till the last quarter of the twentieth and Charles Whish, officers serving under the East India century, continued to maintain that the Creative period in Company, came across traditional practitioners of Indian Indian mathematics ended with Bhaskaracharya II (c.1150 CE) astronomy who seemed to be conversant with several infinite and that Indian mathematics, bereft of any notion of proof, had series for the ratio of the circumference to the diameter of no logical rigour.