Bhaskaracharya's Lilavathi
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Roman Numerals
History of Numbers 1c. I can distinguish between an additive and positional system, and convert between Roman and Hindu-Arabic numbers. Roman Numerals The numeric system represented by Roman numerals originated in ancient Rome (753 BC–476 AD) and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. By the 11th century, the more efJicient Hindu–Arabic numerals had been introduced into Europe by way of Arab traders. Roman numerals, however, remained in commo use well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Roman numerals are still used today, in certain contexts. See: Modern Uses of Roman Numerals Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols: The numbers 1 to 10 are expressed in Roman numerals as: I, II, III, IV, V, VI, VII, VIII, IX, X. This an additive system. Numbers are formed by combining symbols and adding together their values. For example, III is three (three ones) and XIII is thirteen (a ten plus three ones). Because each symbol (I, V, X ...) has a Jixed value rather than representing multiples of ten, one hundred and so on (according to the numeral's position) there is no need for “place holding” zeros, as in numbers like 207 or 1066. Using Roman numerals, those numbers are written as CCVII (two hundreds, plus a ive and two ones) and MLXVI (a thousand plus a ifty plus a ten, a ive and a one). -
Ancient Indian Mathematical Evolution Since Counting
Journal of Statistics and Mathematical Engineering e-ISSN: 2581-7647 Volume 5 Issue 3 Ancient Indian Mathematical Evolution since Counting 1 2 Sankar Prasad Mukherjee , Sandip Ghanta* 1Research Guide, 2Research Scholar 1,2Department of Mathematics, Seacom Skills University, Kolkata, West Bengal, India Email: *[email protected] DOI: Abstract This paper is an endeavor how chronologically since inception and into growth of mathematics occurred in Ancient India with an effort of counting to establish the numeral system through different ages, i.e., Rigveda, Yajurvada, Buddhist, Indo-Bactrian, Bramhi, Gupta and Devanagari Periods. Ancient India’s such contribution was of immense value helped to accelerate the progress of Mathematical development up to modern age as we see today. Keywords: Brahmi numerals, centesimal scale, devanagari, rigveda, kharosthi numerals, yajurveda INTRODUCTION main striking feature being counting and This research paper is an endeavor to evolution of numeral system thereby. synchronize all the historical research with essence of pre-historic and post-historic Mathematical Evolution in Vedic Period respectively interwoven into a texture of Decimal Number System in the Rigveda evolution process of Mathematics. The first Numbers are represented in decimal system form of writing human race was not (i.e., base 10) in the Rigveda, in all other literature but Mathematics. Arithmetic Vedic treatises, and in all subsequent Indian what is today was felt as an essential need texts. No other base occurs in ancient for day to day necessity of human race. In Indian texts, except a few instances of base various countries at various point of time, 100 (or higher powers of 10). -
Minutes of the Meeting of the Expert Committee Held on 14Th, 15Th,17Th and 18Th October, 2013 Under the Performing Arts Grants Scheme (PAGS)
No.F.10-01/2012-P.Arts (Pt.) Ministry of Culture P. Arts Section Minutes of the Meeting of the Expert Committee held on 14th, 15th,17th and 18th October, 2013 under the Performing Arts Grants Scheme (PAGS). The Expert Committee for the Performing Arts Grants Scheme (PAGS) met on 14th, 15th ,17thand 18th October, 2013 to consider renewal of salary grants to existing grantees and decide on the fresh applications received for salary and production grants under the Scheme, including review of certain past cases, as recommended in the earlier meeting. The meeting was chaired by Smt. Arvind Manjit Singh, Joint Secretary (Culture). A list of Expert members present in the meeting is annexed. 2. On the opening day of the meeting ie. 14th October, inaugurating the meeting, Sh. Sanjeev Mittal, Joint Secretary, introduced himself to the members of Expert Committee and while welcoming the members of the committee informed that the Ministry was putting its best efforts to promote, develop and protect culture of the country. As regards the Performing Arts Grants Scheme(earlier known as the Scheme of Financial Assistance to Professional Groups and Individuals Engaged for Specified Performing Arts Projects; Salary & Production Grants), it was apprised that despite severe financial constraints invoked by the Deptt. Of Expenditure the Ministry had ensured a provision of Rs.48 crores for the Repertory/Production Grants during the current financial year which was in fact higher than the last year’s budgetary provision. 3. Smt. Meena Balimane Sharma, Director, in her capacity as the Member-Secretary of the Expert Committee, thereafter, briefed the members about the salient features of various provisions of the relevant Scheme under which the proposals in question were required to be examined by them before giving their recommendations. -
Crowdsourcing
CROWDSOURCING The establishment of the ZerOrigIndia Foundation is predicated on a single premise, namely, that our decades-long studies indicate that there are sound reasons to assume that facilitating further independent scientific research into the origin of the zero digit as numeral may lead to theoretical insights and practical innovations equal to or perhaps even exceeding the revolutionary progress to which the historic emergence of the zero digit in India somewhere between 200 BCE and 500 CE has led across the planet, in the fields of mathematics, science and technology since its first emergence. No one to date can doubt the astounding utility of the tenth and last digit to complete the decimal system, yet the origin of the zero digit is shrouded in mystery to this day. It is high time, therefore, that a systematic and concerted effort is undertaken by a multidisciplinary team of experts to unearth any extant evidence bearing on the origin of the zero digit in India. The ZerOrigIndia Foundation is intended to serve as instrument to collect the requisite funds to finance said independent scientific research in a timely and effective manner. Research Academics and researchers worldwide are invited to join our efforts to unearth any extant evidence of the zero digit in India. The ZerOrigIndia Foundation will facilitate the research in various ways, chief among which is to engage in fundraising to finance projects related to our objective. Academics and researchers associated with reputed institutions of higher learning are invited to monitor progress reported by ZerOrigIndia Foundation, make suggestions and/or propose their own research projects to achieve the avowed aim. -
Dr. Babasaheb Ambedkar Writings & Speeches Vol. 4
Babasaheb Dr. B.R. Ambedkar (14th April 1891 - 6th December 1956) BLANK DR. BABASAHEB AMBEDKAR WRITINGS AND SPEECHES VOL. 4 Compiled by VASANT MOON Dr. Babasaheb Ambedkar : Writings and Speeches Vol. 4 First Edition by Education Department, Govt. of Maharashtra : October 1987 Re-printed by Dr. Ambedkar Foundation : January, 2014 ISBN (Set) : 978-93-5109-064-9 Courtesy : Monogram used on the Cover page is taken from Babasaheb Dr. Ambedkar’s Letterhead. © Secretary Education Department Government of Maharashtra Price : One Set of 1 to 17 Volumes (20 Books) : Rs. 3000/- Publisher: Dr. Ambedkar Foundation Ministry of Social Justice & Empowerment, Govt. of India 15, Janpath, New Delhi - 110 001 Phone : 011-23357625, 23320571, 23320589 Fax : 011-23320582 Website : www.ambedkarfoundation.nic.in The Education Department Government of Maharashtra, Bombay-400032 for Dr. Babasaheb Ambedkar Source Material Publication Committee Printer M/s. Tan Prints India Pvt. Ltd., N. H. 10, Village-Rohad, Distt. Jhajjar, Haryana Minister for Social Justice and Empowerment & Chairperson, Dr. Ambedkar Foundation Kumari Selja MESSAGE Babasaheb Dr. B.R. Ambedkar, the Chief Architect of Indian Constitution was a scholar par excellence, a philosopher, a visionary, an emancipator and a true nationalist. He led a number of social movements to secure human rights to the oppressed and depressed sections of the society. He stands as a symbol of struggle for social justice. The Government of Maharashtra has done a highly commendable work of publication of volumes of unpublished works of Dr. Ambedkar, which have brought out his ideology and philosophy before the Nation and the world. In pursuance of the recommendations of the Centenary Celebrations Committee of Dr. -
Numerical Notation: a Comparative History
This page intentionally left blank Numerical Notation Th is book is a cross-cultural reference volume of all attested numerical notation systems (graphic, nonphonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defi es progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifi es fi ve basic types of numerical notation systems, using a cultural phylo- genetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are prima- rily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness and avoidance of ambiguity, which also apply to writing systems. Th e transformation and replacement of numerical notation systems relate to spe- cifi c social, economic, and technological changes, such as the development of the printing press and the expansion of the global world-system. Stephen Chrisomalis is an assistant professor of anthropology at Wayne State Uni- versity in Detroit, Michigan. He completed his Ph.D. at McGill University in Montreal, Quebec, where he studied under the late Bruce Trigger. Chrisomalis’s work has appeared in journals including Antiquity, Cambridge Archaeological Jour- nal, and Cross-Cultural Research. He is the editor of the Stop: Toutes Directions project and the author of the academic weblog Glossographia. Numerical Notation A Comparative History Stephen Chrisomalis Wayne State University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521878180 © Stephen Chrisomalis 2010 This publication is in copyright. -
N Murali Krishna Superconductivity: Penetration Depth and Physical Properties
UNIVERSITY OF HYDERABAD 23rd ANNUAL REPORT Report on the working of the University (1 April 1997 to 31 March-1998) CENTRAL UNIVERSITY P.O HYDERABAD - 500 046 Visitor President of India Chief Rector Governor of Andhra Pradesh Chancellor Abid Hussain (upto 8.12.1997) Romila Thapar (from 9.12.1997) Vice Chancellor Goverdhan Mehta, Ph.D. (Pune) Deans of Schools Chemistry P.S.Zacharias, Ph.D. (I.I.T. Kanpur) Life Sciences A.R.Reddy, Ph.D. (Osmania) (upto 9.1.1998) R.P.Shanna, Ph.D.(J.N.U.) (from 10.1.1998) Mathematics & C.Musili, Ph.D. (T.I.F.R.Bombay) Computer/Information Sciences Physics K.N.Shrivatsava, Ph.D. (I.I.T. Kanpur) (upto 1.1.1998) A.K.Bhatnagar, Ph.D. (Maryland) (I/c. from 2.1.1998) Humanities Y.V.Ramana Rao, Ph.D. (S.V.U) (upto 31.12.1997) K.K.Ranganadhacharyulu, Ph.D. (Osmania) (from 1.1.1998) Social Sciences T.R.Sharma Ph.D. (B.H.U.) Sarojini Naidu School of BP.Sanjay Ph.D. (Simon Fraser) Performing Arts, Fine Arts & Communication Registrar M.Madan Gopal, I.A.S. Finance Officer J.Lakshinipathi, I.A. &. A.S. Librarian E. Rama Reddy CONTACTS Deans of the Schools Prof. C.Musili, School of Mathematics & Prof. K.K.Ranganadhacharyulu, Computer/Information Sciences School of Humanities Telephone : (040) 3010560,3010500/4000 Telephone : (040)3010003,3010500/3300 E-Mail : [email protected] E-Mail : [email protected] Prof. A.K. Bhatnagar, School of Physics Prof. V.V.N.Somayajulu, School of Social Sciences Telephone : (040)3010227,3010500/4300 Telephone; (040) 3010853, 3010500/3000 E-Mail : [email protected] E-Mail ; [email protected] Prof. -
Equation Solving in Indian Mathematics
U.U.D.M. Project Report 2018:27 Equation Solving in Indian Mathematics Rania Al Homsi Examensarbete i matematik, 15 hp Handledare: Veronica Crispin Quinonez Examinator: Martin Herschend Juni 2018 Department of Mathematics Uppsala University Equation Solving in Indian Mathematics Rania Al Homsi “We owe a lot to the ancient Indians teaching us how to count. Without which most modern scientific discoveries would have been impossible” Albert Einstein Sammanfattning Matematik i antika och medeltida Indien har påverkat utvecklingen av modern matematik signifi- kant. Vissa människor vet de matematiska prestationer som har sitt urspring i Indien och har haft djupgående inverkan på matematiska världen, medan andra gör det inte. Ekvationer var ett av de områden som indiska lärda var mycket intresserade av. Vad är de viktigaste indiska bidrag i mate- matik? Hur kunde de indiska matematikerna lösa matematiska problem samt ekvationer? Indiska matematiker uppfann geniala metoder för att hitta lösningar för ekvationer av första graden med en eller flera okända. De studerade också ekvationer av andra graden och hittade heltalslösningar för dem. Denna uppsats presenterar en litteraturstudie om indisk matematik. Den ger en kort översyn om ma- tematikens historia i Indien under många hundra år och handlar om de olika indiska metoderna för att lösa olika typer av ekvationer. Uppsatsen kommer att delas in i fyra avsnitt: 1) Kvadratisk och kubisk extraktion av Aryabhata 2) Kuttaka av Aryabhata för att lösa den linjära ekvationen på formen 푐 = 푎푥 + 푏푦 3) Bhavana-metoden av Brahmagupta för att lösa kvadratisk ekvation på formen 퐷푥2 + 1 = 푦2 4) Chakravala-metoden som är en annan metod av Bhaskara och Jayadeva för att lösa kvadratisk ekvation 퐷푥2 + 1 = 푦2. -
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]. -
Some Interesting Facts, Myths and History of Mathematics
International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: 2321 – 4767 P-ISSN: 2321 - 4759 www.ijmsi.org Volume 4 Issue 6 || August. 2016 || PP-54-68 Some Interesting Facts, Myths and History of Mathematics Singh Prashant1 1(Department of Computer Science, Institute of Science, Banaras Hindu University) ABSTRACT : This paper deals with primary concepts and fallacies of mathematics which many a times students and even teachers ignore. Also this paper comprises of history of mathematical symbols, notations and methods of calculating time. I have also included some ancient techniques of solving mathematical real time problems. This paper is a confluence of various traditional mathematical techniques and their implementation in modern mathematics. I. INTRODUCTION I have heard my father saying that ―Mathematics is the only genuine subject as it does not change with boundary of countries‖. It is lucrative just because of its simplicity. Galileo once said, ―Mathematics is the language with which God wrote the Universe.‖ He was precise in calling mathematics a language, because like any dialect, mathematics has its own rubrics, formulas, and nuances. In precise, the symbols used in mathematics are quite unique to its field and are profoundly engrained in history. The following will give an ephemeral history of some of the greatest well-known symbols employed by mathematics. Categorized by discipline within the subject, each section has its own interesting subculture surrounding it. Arithmetic is the most rudimentary part of mathematics and covers addition, subtraction, multiplication, and the division of numbers. One category of numbers are the integers, -n,…-3,-2,-1,0,1,2,3,…n , where we say that n is in .The capital letter Z is written to represent integers and comes from the German word, Zahlen, meaning numbers. -
Påˆini and Euclid: Reflections on Indian Geometry* (Published In: Journal of Indian Philosophy 29 (1-2; Ingalls Commemoration Volume), 2001, 43-80)
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Serveur académique lausannois Påˆini and Euclid 1 JOHANNES BRONKHORST Påˆini and Euclid: reflections on Indian geometry* (published in: Journal of Indian Philosophy 29 (1-2; Ingalls Commemoration Volume), 2001, 43-80) Professor Ingalls — in an article called "The comparison of Indian and Western philosophy" — made the following interesting observation (1954: 4): "In philosophizing the Greeks made as much use as possible of mathematics. The Indians, curiously, failed to do this, curiously because they were good mathematicians. Instead, they made as much use as possible of grammatical theory and argument." This observation should not — as goes without saying in our day and age — be read as a description of the Indian “genius” as opposed to that of the Greeks (at least not in some absolute sense), but as a reminder of the important roles that mathematics and linguistics have played as methodical guidelines in the development of philosophy in Greece and in India respectively. Ingalls appears to have been the first to draw attention to this important distinction. He was not the last. Ingalls's observation has been further elaborated by J. F. (= Frits) Staal in a few articles (1960; 1963; 1965).1 Staal focuses the discussion on two historical persons in particular, Euclid and Påˆini, both of whom — as he maintains — have exerted an important, even formative, influence on developments in their respective cultures. Staal also broadens the horizon by drawing other areas than only philosophy into the picture. To cite his own words (1965: 114 = 1988: 158): "Historically speaking, Påˆini's method has occupied a place comparable to that held by Euclid's method in Western thought. -
International Conference on the 900Th Birth Anniversary of Bhāskarācārya
International Conference on the 900th Birth Anniversary of Bhāskarācārya 19, 20, 21 September 2014 ABSTRACTS Vidya Prasarak Mandai Vishnu Nagar, Naupada, Thane 400602 2 I BHĀSKARĀCĀRYA’S LIFE AND TIMES A. P. JAMKHEDKAR, Mumbai. ‘Learning and Patronage in 12th -13th Century A.D.: Bhaskarācarya and the Śāndilya Family, A Case Study’ … … … … … 5 II BHASKARĀCĀRYA’S POETIC GENIUS Pierre-Sylvain FILLIOZAT, Paris. ‘The poetical face of the mathematical and astronomical works of Bhāskarācārya’ … … … … … … … … 7 K. S. BALASUBRAMANIAN, Chennai. ‘Bhāskarācārya as a Poet’ … … … … 8 GEETHAKUMARI, K. K., Calicut. ‘Contribution of Līlāvatī to Prosody’ … … … 9 Poonam GHAI, Dhampur. ‘Līlāvatī men Kāvya-saundarya’ … … … … … … 10 III THE LĪLĀVATĪ K. RAMASUBRAMANIAN, Mumbai. ‘The Līlā of the Līlāvatī: A Beautiful Blend of Arithmetic, Geometry and Poetry’ … … … … … … … … … 11 PADMAVATAMMA, Mysore. ‘A Comparative Study of Bhāskarācārya’s Līlāvatī and Mahāvīrācārya’s Gaṇitasārasaṁgraha’… … … … … … … … 11 K. RAMAKALYANI, Chennai. ‘Gaṇeśa Daivajña’s Upapattis on Līlāvatī’ … … 12 Anil NARAYANAN, N., Calicut. ‘Parameswara’s Unpublished Commentary on Lilavati: Perceptions and Problems’ … … … … … … … … … … … 13 P. RAJASEKHAR & LAKSHMI, V. Calicut. ‘Līlāvatī and Kerala School of Mathematics’ 14 N. K. Sundareswaran & P. M. Vrinda, Calicut. ‘Malayalam Commentaries on Līlāvatī – A Survey of Manuscripts in Kerala’ … … … … … … 15 Shrikrishna G. DANI, Mumbai. ‘Mensuration of Quadrilaterals in Lilavati’ … … 16 Takanori KUSUBA, Osaka. ‘Aṅkapāśa in the Līlāvatī’ … … … … … … … 17 Medha Srikanth LIMAYE, Mumbai. Use of Bhūta-Saṅkhyās (Object Numerals) in Līlāvatī of Bhāskarācārya’ … … … … … … … … … … 17 Sreeramula Rajeswara SARMA, Düsseldorf. ‘The Legend of Līlāvatī’ … … … 17 IV THE BĪJAGAṆITA Sita Sundar RAM, Chennai. ‘Bījagaṇita of Bhāskara’ … … … … … … … 19 K. VIDYUTA, Chennai. ‘Sūryaprakāśa of Sūryadāsa – a Review’ … … … … 20 Veena SHINDE-DEORE & Manisha M. ACHARYA, Mumbai. ‘Bhaskaracharya and Varga Prakriti: the equations of the type ax2 + b = cy2’ … … … … … 20 K.