Math, Science, and Technology in India—From the Ancient to The
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A Quartically Convergent Square Root Algorithm: an Exercise in Forensic Paleo-Mathematics
A Quartically Convergent Square Root Algorithm: An Exercise in Forensic Paleo-Mathematics David H Bailey, Lawrence Berkeley National Lab, USA DHB’s website: http://crd.lbl.gov/~dhbailey! Collaborator: Jonathan M. Borwein, University of Newcastle, Australia 1 A quartically convergent algorithm for Pi: Jon and Peter Borwein’s first “big” result In 1985, Jonathan and Peter Borwein published a “quartically convergent” algorithm for π. “Quartically convergent” means that each iteration approximately quadruples the number of correct digits (provided all iterations are performed with full precision): Set a0 = 6 - sqrt[2], and y0 = sqrt[2] - 1. Then iterate: 1 (1 y4)1/4 y = − − k k+1 1+(1 y4)1/4 − k a = a (1 + y )4 22k+3y (1 + y + y2 ) k+1 k k+1 − k+1 k+1 k+1 Then ak, converge quartically to 1/π. This algorithm, together with the Salamin-Brent scheme, has been employed in numerous computations of π. Both this and the Salamin-Brent scheme are based on the arithmetic-geometric mean and some ideas due to Gauss, but evidently he (nor anyone else until 1976) ever saw the connection to computation. Perhaps no one in the pre-computer age was accustomed to an “iterative” algorithm? Ref: J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity}, John Wiley, New York, 1987. 2 A quartically convergent algorithm for square roots I have found a quartically convergent algorithm for square roots in a little-known manuscript: · To compute the square root of q, let x0 be the initial approximation. -
Accidental Prime Minister
THE ACCIDENTAL PRIME MINISTER THE ACCIDENTAL PRIME MINISTER THE MAKING AND UNMAKING OF MANMOHAN SINGH SANJAYA BARU VIKING Published by the Penguin Group Penguin Books India Pvt. Ltd, 11 Community Centre, Panchsheel Park, New Delhi 110 017, India Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, M4P 2Y3, Canada (a division of Pearson Penguin Canada Inc.) Penguin Books Ltd, 80 Strand, London WC2R 0RL, England Penguin Ireland, 25 St Stephen’s Green, Dublin 2, Ireland (a division of Penguin Books Ltd) Penguin Group (Australia), 707 Collins Street, Melbourne, Victoria 3008, Australia (a division of Pearson Australia Group Pty Ltd) Penguin Group (NZ), 67 Apollo Drive, Rosedale, Auckland 0632, New Zealand (a division of Pearson New Zealand Ltd) Penguin Group (South Africa) (Pty) Ltd, Block D, Rosebank Offi ce Park, 181 Jan Smuts Avenue, Parktown North, Johannesburg 2193, South Africa Penguin Books Ltd, Registered Offi ces: 80 Strand, London WC2R 0RL, England First published in Viking by Penguin Books India 2014 Copyright © Sanjaya Baru 2014 All rights reserved 10 9 8 7 6 5 4 3 2 1 The views and opinions expressed in this book are the author’s own and the facts are as reported by him which have been verifi ed to the extent possible, and the publishers are not in any way liable for the same. ISBN 9780670086740 Typeset in Bembo by R. Ajith Kumar, New Delhi Printed at Thomson Press India Ltd, New Delhi This book is sold subject to the condition that -
College Profile
TRAINING AND PLACEMENT OFFICE UNIVERSITY VISVESVARAYA COLLEGE OF ENGINEERING (UVCE) (Est.: 1917) BANGALORE UNIVERSITY, K.R.CIRCLE, BENGALURU - 560 001 Greetings from UVCE!! We are privileged to inform that UVCE has celebrated 100 successful years and counting. We are happy to invite your esteemed organization to visit our campus for recruitment to hire best of the talents for the academic year 2020-21. We await a positive response from your end and will be happy to answer any queries. A brief information about our institution is given below. HISTORY In 1917, the then Diwan of Mysore Sir M. Visvesvaraya felt a need to have an engineering college in the state, as the Civil Engineering College at Madras and College of Engineering at Poona were unable to accommodate enough students from the then Mysore State. He started the college in 1917 in Bangalore under the University of Mysore. It was started as the School of Engineering with 20 students each in Civil and Mechanical Engineering branches. It was the fifth engineering college to be started in India and the first one in Mysore State. In 1965, the name of the college was changed to University Visvesvaraya College of Engineering after its founder. It is currently the only constituent college of Bangalore University. The name UVCE is very popular in the field of technical education in Karnataka. In its existence of 103 years, the college has a history of great reputation and countless number of alumni. It has produced many eminent engineers, who have occupied coveted positions in industries, research labs and various prestigious institutions in India and abroad. -
From Dorota Borowa's Ice Painting Workshop. TABLE of CONTENTS
15.12.19 - 30.01.20 SUB MERGE From Dorota Borowa's Ice Painting workshop. TABLE OF CONTENTS ABOUT SUBMERGE 4 OVERVIEW 6 THEMES AT SUBMERGE 12 CURATED PROGRAMMES AT SUBMERGE - CONFLUENCE 136 - SOAK 168 MEDIATORS 192 TAKE IT FURTHER 196 COLLABORATORS 202 *Please note that the images used throughout the report are the copyright of the photographer or Science Gallery Bengaluru and are not available under Creative Commons People and Water by T. S. Satyan and Jyoti Bhatt. Courtesy of Museum of Art and Photography (MAP). ABOUT SUBMERGE On 15 December 2019, we opened our first exhibition season on water, SUBMERGE, to the public. Through this exhibition, we supported the Year of Water initiative as observed by the Government of Karnataka. It also featured H2O Today, a popular traveling exhibition by the Smithsonian Institution. We encouraged visitors to explore the collective experiences of water and refIect on future challenges through a range of dynamic exhibits and workshops. We presented 15 exhibits spread across three floors of Bangalore International Centre, which examined the role of water in our lives, beyond the value that we derive from it. These exhibits were brought to life through 45 connected programmes such as workshops, lectures, master classes, film screenings and musical performances. Participants engaged with the latest research and thinking on water, and examined its cultural significance, by interacting with scholars and artists from around the world. We also provoked them to begin a dialogue on water as an urgent concern for the city of Bengaluru, and global challenge of the Anthropocene. Ice Painting by Dorota Borowa. -
Current Affairs 2013- January International
Current Affairs 2013- January International The Fourth Meeting of ASEAN and India Tourism Minister was held in Vientiane, Lao PDR on 21 January, in conjunction with the ASEAN Tourism Forum 2013. The Meeting was jointly co-chaired by Union Tourism Minister K.Chiranjeevi and Prof. Dr. Bosengkham Vongdara, Minister of Information, Culture and Tourism, Lao PDR. Both the Ministers signed the Protocol to amend the Memorandum of Understanding between ASEAN and India on Strengthening Tourism Cooperation, which would further strengthen the tourism collaboration between ASEAN and Indian national tourism organisations. The main objective of this Protocol is to amend the MoU to protect and safeguard the rights and interests of the parties with respect to national security, national and public interest or public order, protection of intellectual property rights, confidentiality and secrecy of documents, information and data. Both the Ministers welcomed the adoption of the Vision Statement of the ASEAN-India Commemorative Summit held on 20 December 2012 in New Delhi, India, particularly on enhancing the ASEAN Connectivity through supporting the implementation of the Master Plan on ASEAN Connectivity. The Ministers also supported the close collaboration of ASEAN and India to enhance air, sea and land connectivity within ASEAN and between ASEAN and India through ASEAN-India connectivity project. In further promoting tourism exchange between ASEAN and India, the Ministers agreed to launch the ASEAN-India tourism website (www.indiaasean.org) as a platform to jointly promote tourism destinations, sharing basic information about ASEAN Member States and India and a visitor guide. The Russian Navy on 20 January, has begun its biggest war games in the high seas in decades that will include manoeuvres off the shores of Syria. -
Bakhshali Manuscript
THE BAKHSHALI P 1' AN ANCIENT TREATISE OF INDIAN Alt I'I'I I N 4F,' EDITED BY Svami Satya Prakash Sarasvat I and 00 Usha,jyotishmati, M. Sc., D. Phil. Dr. Rataa Kumari Svadhyaya Sansthani ALLAHABAD. PUBLISHE S BY Dr. Ratn Kumari Svadhyaya Sansthana Vijnaua Parishad Buildings Maharshi Dayanand Marg Allahabad-211002 Phone : 54413 FIRST EDITION 1979 Price Rs. 50/-( £ 3.5 or $ 7 ) Printed at :- ARVIND PRINTERS 20-1), Bell Road, Allahabad, Phone Not 3711 CDr `-Patna umari Born 20-3- 19 12 Died 2-12-1964 PREFACE Dr. Ratna Kumari, M. A., D. Phil. was deeply interested in education, higher research and scholarship, and when she died in 1964, the Director of the Research Institute of Ancient Scientific Studies, Now Delhi, graciously agreed to publish in her commemo- ration a Series to be known as the "Dr. Raffia Kumari PubllcaNnu Series", and tinder this arrangement, the five volumes published were: Satapatha Brahmanain.Vol. I, 11 and III (1967, 1969, 19711): ltaudhayana Sulba Sutram (1968) and the Apastanrba Sulba Sutruun (1968).Itis to be regretted that in1971, Pundit Rain Swarnp Sharnta, the Director of the Institute died and shortly afterwards, the activities of the Institute came to a close.In 1971, from an endowment created by the relations of late Dr. Ratna Kurnari, Dr. Ratna Kumari Svadhyaya Sansthana, a research orgunicution for promotion of higher studiesamongstladies,wasostahll. shed at Allahabad, with Sri Anand Prakash, the younger son of 1)r. Ratna Kumari as the firstPresident.Svumi Satya Prukunlt (formerly, Prof. Dr. Satya Prakash)has authorisedDr.Ratna Kumari Svadhyaya Sansthana to publish several of his works, plirti. -
Roddam Narasimha
LIVING LEGENDS IN INDIAN SCIENCE Roddam Narasimha G. S. Bhat and K. R. Sreenivasan Professor Roddam Narasimha, known as hone mastery over a subject by returning are reprinted even today. While RN did ‘Roddam’ to his close colleagues and to it several times over, and the unspoken not learn much science directly from his ‘RN’ to his students, has been an out- moral authority he exerts on his col- father, the latter’s example and attitude – standing teacher1, a world-class res- leagues, are not easy to discern. The pub- scientifically modern, socially liberal and earcher2, a dynamic leader3, and a lic record of his service to the country is culturally conservative – seem to have builder of institutions4; while his profes- somewhat sporadic11. A few autobio- played a great role in shaping the young sional interests are primarily in fluid dy- graphical notes12 that exist shed only RN12. His mother, R. N. Leela Devi, did namics, they extend significantly to other modest light on his formative life and his not attend school beyond age ten, but she areas such as formal aspects of educa- involvement with Indian scientific enter- was well read and sophisticated: the tion5, philosophy6, history and history of prise. One hopes that a comprehensive prayers she taught her children to recite Indian science7, India’s nuclear policy account of all facets of his life and before bed time were for intelligence and and national security8, and others; and he endeavours will appear in the future. knowledge12. has dispensed advice and wisdom to the This short article cannot do full justice to RN studied at Acharya Pathashala, a highest circles in the country and his them and is only a partial account reputed private school in Bangalore13. -
In How Many Days Will He Meet His Wife?
Journal of Humanistic Mathematics Volume 11 | Issue 1 January 2021 In How Many Days Will He Meet His Wife? Dipak Jadhav Govt. Boys Higher Secondary School, Anjad Distt. Barwani (M. P.) India Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Jadhav, D. "In How Many Days Will He Meet His Wife?," Journal of Humanistic Mathematics, Volume 11 Issue 1 (January 2021), pages 95-112. DOI: 10.5642/jhummath.202101.07 . Available at: https://scholarship.claremont.edu/jhm/vol11/iss1/7 ©2021 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. In How Many Days Will He Meet His Wife? Cover Page Footnote Except for a few changes this paper was presented as an invited talk in International Web-Conference on History of Mathematics, during December 20-22, 2020 organized by Indian Society for History of Mathematics, Delhi, India. This work is available in Journal of Humanistic Mathematics: https://scholarship.claremont.edu/jhm/vol11/iss1/7 In How Many Days Will He Meet His Wife? Dipak Jadhav Govt. -
Secondary Indian Culture and Heritage
Culture: An Introduction MODULE - I Understanding Culture Notes 1 CULTURE: AN INTRODUCTION he English word ‘Culture’ is derived from the Latin term ‘cult or cultus’ meaning tilling, or cultivating or refining and worship. In sum it means cultivating and refining Ta thing to such an extent that its end product evokes our admiration and respect. This is practically the same as ‘Sanskriti’ of the Sanskrit language. The term ‘Sanskriti’ has been derived from the root ‘Kri (to do) of Sanskrit language. Three words came from this root ‘Kri; prakriti’ (basic matter or condition), ‘Sanskriti’ (refined matter or condition) and ‘vikriti’ (modified or decayed matter or condition) when ‘prakriti’ or a raw material is refined it becomes ‘Sanskriti’ and when broken or damaged it becomes ‘vikriti’. OBJECTIVES After studying this lesson you will be able to: understand the concept and meaning of culture; establish the relationship between culture and civilization; Establish the link between culture and heritage; discuss the role and impact of culture in human life. 1.1 CONCEPT OF CULTURE Culture is a way of life. The food you eat, the clothes you wear, the language you speak in and the God you worship all are aspects of culture. In very simple terms, we can say that culture is the embodiment of the way in which we think and do things. It is also the things Indian Culture and Heritage Secondary Course 1 MODULE - I Culture: An Introduction Understanding Culture that we have inherited as members of society. All the achievements of human beings as members of social groups can be called culture. -
The Bakhshālī Manuscript: a Response to the Bodleian Library's Radiocarbon Dating
History of Science in South Asia A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia The Bakhshālī Manuscript: A Response to the Bodleian Library’s Radiocarbon Dating Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk Union College, CNRS & Université Denis-Diderot, Doshisha University, University of Canterbury and University of Alberta MLA style citation form: Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk. “The Bakhshālī Manuscript: A Response to the Bodleian Lib- rary’s Radiocarbon Dating.” History of Science in South Asia, 5.1 (2017): 134–150. doi: 10.18732/H2XT07. Online version available at: https://hssa-journal.org HISTORY OF SCIENCE IN SOUTH ASIA A journal for the history of all forms of scientific thought and action, ancient and modern, inall regions of South Asia, published online at http://hssa-journal.org ISSN 2369-775X Editorial Board: • Dominik Wujastyk, University of Alberta, Edmonton, Canada • Kim Plofker, Union College, Schenectady, United States • Dhruv Raina, Jawaharlal Nehru University, New Delhi, India • Sreeramula Rajeswara Sarma, formerly Aligarh Muslim University, Düsseldorf, Germany • Fabrizio Speziale, Université Sorbonne Nouvelle – CNRS, Paris, France • Michio Yano, Kyoto Sangyo University, Kyoto, Japan Publisher: History of Science in South Asia Principal Contact: Dominik Wujastyk, Editor, University of Alberta Email: [email protected] Mailing Address: History of Science in South Asia, Department of History and Classics, 2–81 HM Tory Building, University of Alberta, Edmonton, AB, T6G 2H4 Canada This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. -
From China to Paris: 2000 Years Transmission of Mathematical Idea S
FROM CHINA TO PARIS: 2000 YEARS TRANSMISSION OF MATHEMATICAL IDEA S EDITED BY YVONNE DOLD-SAMPLONIUS JOSEPH W. DAUBEN MENSO FOLKERTS BENNO VAN DALEN FRANZ STEINER VERLAG STUTTGART FROM CHINA TO PARIS: 2000 YEARS TRANSMISSION OF MATHEMATICAL IDEAS BOETHIUS TEXTE UND ABHANDLUNGEN ZUR GESCHICHTE DER MATHEMATIK UND DER NATURWISSENSCHAFTEN BEGRIJNDET VON JOSEPH EHRENFRIED HOFMANN FRIEDRICH KLEMM UND BERNHARD STICKER HERAUSGEGEBEN VON MENSO FOLKERTS BAND 46 FRANZ STEINER VERLAG STUTTGART 2002 FROM CHINA TO PARIS: 2000 YEARS TRANSMISSION OF MATHEMATICAL IDEAS EDITED BY YVONNE DOLD-SAMPLONIUS JOSEPH W. DAUBEN MENSO FOLKERTS BENNO VAN DALEN FRANZ STEINER VERLAG STUTTGART 2002 Bibliographische Information der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet these Publikation in der Deutschen National- bibliographic; detaillierte bibliographische Daten sind im Internet Uber <http:// dnb.ddb.de> abrufbar. ISBN 3-515-08223-9 ISO 9706 Jede Verwertung des Werkes auBerhalb der Grenzen des Urheberrechtsgesetzes ist unzulhssig and strafbar. Dies gilt insbesondere fair Ubersetzung, Nachdruck. Mikrover- filmung oder vergleichbare Verfahren sowie fi rdie Speicherung in Datenverarbeitungs- anlagen. ® 2002 by Franz Steiner Verlag Wiesbaden GmbH. Sitz Stuttgart. Gedruckt auf s3urefreiem. alterungsbesthndigem Papier. Druck: Druckerei Proff. Eurasburg. Printed in Germany Table of Contents VII Kurt Vogel: A Surveying Problem Travels from China to Paris .................... 1 Jens Hoyrup: Seleucid Innovations in the Babylonian "Algebraic" Tradition and their -
Academy News
Proc Indian Natn Sci Acad 80 No. 1 March 2014 pp. 173-178 © Printed in India. 10.16943/ptinsa/2014/v80i1/55095 Academy News INTERNATIONAL ACTIVITIES of Professor DK Pandey, Department of Geology, University of Rajasthan. Indian Scientist nominated for various positions of ICSU & its Unions An IUPAC sponsored 27th International Carbohydrate Symposium (ICS 27) was held at Dr. V Prakash, Distinguished Scientist of CSIR- the Indian Institute of Science, Bangalore during India at JSS-MVP, JSS Technical Institution January 12-17, 2014 under the convenorship of Campus, Mysore is nominated for the position Professor N Jayaraman, Department of Organic of President-Elect as well as Council Member Chemistry, Indian Institute of Sciences, of International Union of Food Science & Bangalore. Technology (IUFoST) for the term 2014-2016. An International Workshop on 4th Current Professor S Ananthakrishnan, FNA is re- Trends in Structural Biology (CTSB) in Multi nominated for the position of Vice-President, Drug Resistant Bacterial Therapeutics and International Union of Radio Science (URSI) Thrombosis was organized under the for the term 2014-2017. convenorship of Dr Sujata Sharma, Department Dr. Madhavan Nair Rajeevan, Adviser and of Biophysics, All India Institute of Medical Scientist G, Ministry of Earth Sciences, New Sciences, New Delhi during February 27-28, Delhi is nominated for the membership of World 2014. This was sponsored by INSA-National Climate Research Programme(WCRP) Joint Committee for International Union of Scientific Committee. Crystallography (IUCr) as an activity to mark International Year of Crystallography 2014. Workshop/Symposia/Conference supported by the Academy Support to Visiting Scientists during January 2014 An URSI sponsored Regional conference on The Academy supported 3 Indian scientists namely Radio Science (RCRS-2014) was held at the Dr.