
A Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact
Publication Year: 2009
DOI: http://dx.doi.org/10.4135/9788132108085
Subject: Mathematics, South Asia Studies
- Chapters
- Front Matter
- Back Matter
- Subject Index
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- 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
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Copyright
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.
p. cm.
Includes bibliographical references and index.
1. Mathematics—India—Kerala—History. 2. Mathematics, Medieval. 3. Astronomy, Medieval—India—Kerala. I. Title.
QA27.I4J67 510.954′830902—dc22 2009 2009035222
ISBN: 978-81-321-0168-0 (HB)
The SAGE Team: Rekha Natarajan, Sushmita Banerjee and Trinankur Banerjee
Dedication
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.
List of Tables and Figures
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
Figures- 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
- 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
Acknowledgements
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.
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Bibliography
1993) ‘Charles Dodgson's Geometric Approach to Arctangent Relations for Π’, Historia Mathematica, 20(2): 151–59. http://dx.doi.org/10.1006/hmat.1993.1013(2000) ‘Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications’, Journal of Natural Geometry, 20(1): 77–104., , and (2004) ‘Eurocentrism in the History of Mathematics: The Case of the Kerala School’, Race and Class, 45(4): 45–60. http://dx.doi.org/10.1177/0306396804043866and (2009a) ‘A Report of the Investigation on the Possibility of the Transmission of the Medieval Kerala Mathematics to Europe’, in G.G.Joseph (ed.), Kerala Mathematics: Its History and Possible Transmission to Europe, pp. 257–76. Delhi: B. R Publishing Corporation.and (2009b) ‘Kerala Mathematics and its Possible Transmission to Europe’, in Ernest, B.Greer and B.Sriraman, Critical Issues in Mathematics Education. Charlotte, NC: Information Age Publishing.and (1068) Science in the Medieval World, translated by S.I.Salem and A.Kumar. Austin: University of Texas Press, 1991.(c.Apte, V.G. (ed.) (1937) Lilavati of Bhaskara II. Anandasrama Sanskrit Series, 107. Pune: Anandasrama Press.The Aryabhata Group (2002) ‘Transmission of the Calculus from Kerala to Europe’, proceedings of the International Seminar and Colloquium on 1500 Years of Aryabhateeyam, Kerala Sastra Sahitya Parishad, Kochi, pp. 33–48.1994) Royal Life in Manasollasa. Delhi: Sundeep Prakashan., (1976) ‘Madhava's sine and cosine sereis’, Indian Journal of History of Science, 11(1): 54–57.(Bag, A.K. and S.R.Sharma (eds). (2003) The Concept of Sunya. Delhi: Aryan Books.2009) ‘Establishing Transmissions: Some Methodological Issues’, in G.G.Joseph (ed.), Kerala Mathematics: Its History and Possible Transmission to Europe, pp. 155–180. Delhi: B. R Publishing Corporation.(1994) Indian Mathematics and Astronomy. Bangalore: Jnana Deep Publications.(1992) Studi su filosofia e scienza dei gesuiti in Italia 1540–1632 (Studies on Science and Philosophy of hte Jesuits in Italy, 1540–1632). Rome: Bulzoni Editore.(2009) ‘The Jesuit Mathematicians in India (1578–1650) as Possible Intermediaries between European and Indian Mathematical Traditions’, in G.G.Joseph (ed.), Kerala Mathematics: Its History and Possible Transmission to Europe, pp. 277–306. Delhi: B.R Publishing.(1992) Corrispondenza/Christoph Clavius; edizione critica a cura. Pisa: Università di Pisa, Dipartimento di matematica.and . (1987) The Origins of the Infinitesimal Calculus. Oxford: Pergamom.(1914) ‘A Comparative Study of the Early Treatises Introducing into Europe the Hindu Art of Reckoning’, Ph.D. Thesis, University of Michigan, Rumford Press.(1823) A Historical View of the Hindu Astronomy. Calcutta: Baptist Mission Press.(1986), Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag.(2007) ‘Mathematics in Medieval Islam’, in V.Katz (ed.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam, A Sourcebook. Princeton: Princeton University Press.(1987) Black Athena. London: Free Association Books.(1973) Matteo Ricci's Scientific Contribution to China. Westport, CT: Hyperion Press,(1030) India, translated by QeyamuddinAhmad, New Delhi: National Book Trust, 1999.(1959) The History of the Calculus and Its Conceptual Development. New York: Dover.(2002) ‘Was Calculus Invented in India?’The College Mathematics Journal (Mathematical Association of America), 33(1): 2–13. http://dx.doi.org/10.2307/1558972(1980) History of Continued Fractions and Pade Approximations. London: Springer-Verlag.(1860) The Surya Siddhanta: A Text-Book of Hindu Astronomy, reprinted, 1997. New Delhi: Motilal Banarsidass Publishers Private Limited.(2002) ‘Indian Numerals in the Mediterranean Basin in the Twelfth Century, with Special Reference to the “Eastern Forms”’, in Y.Dold-Samplonius, J.W.Dauben, M.Folkerts and B.van Dalen (eds), From China to Paris: 2000 Years’ Transmission of Mathematical Ideas, pp. 237–88. Stuttgart: Steiner.(1999) A Contextual History of Mathematics to Euler. New Jersey: Prentice Hall.(1892) Vorlesungen über Geschichte der Mathematik, 4 vols; vol. II, 1892,(2nd edition, 1900. Leipzig: Teubner.1956) Karanapaddhati of Putumana Somayaji. Madras: Govt. Oriental Mss Library.(1873) Miscellaneous Essays, 2 vols. London: Allen and Company.(1969) Jesuit Letters and Indian History 1542–1773. Bombay: Oxford University Press.(1982) Obras completas de D. Joao de Castro, vol. IV. Coimbra: University of Coimbra.and (Correspondance du Marin Mersenne. (1945-) Correspondance du Marin Mersenne, 18 volumes. Paris. Presses Universitaires de France.1984) Cross Cultural Trade in World History. London: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511661198, (1930) The Aryabhatiya of Aryabhatam, translated into English with notes. Chicago: The University of Chicago Press.(1927) ‘Early History of the Arithmetic of Zero and Infinity in India’, Bulletin of the Calcutta Mathematical Society, 18: 165–76.(1932) ‘Elder Aryabhata's Role for the Solution of Indeterminate Equations of the First Degree’, Bulletin of the Calcutta Mathematical Society, 24: 19–36.(1954) The Geometry, translated from French and Latin by David EugeneSmith and Marcia L.Latham. Dover: New York.(Deva Sastri, B. (ed.) (1989) Siddhanta-Siromani, Kashi Sanskrit Series, 72. Varanasi: Chauklamba Sanskrit Sanstan.1960) Galileo in China: Relations through the Roman College between Galileo and the Jesuit Scientist-Missionaries (1610–1640), translated by R.Suter and M.Sciascia. Harvard University Press., (1933) Gar(akatarangi
i, revised edition. Benares: B.K. Shastri.
1979) The Historical Development of the Calculus. New York: Springer-Verlag.(1977) ‘The Area of a Triangle and the Volume of a Pyramid as well as the Area of a Circle and the Surface of the Hemisphere in the Mathematics of Aryabhata I’, Indian Journal of the History of Science, 12(2): 232–36.(2009) ‘The Philosophy of Mathematics, Values and Keralese Mathematics’, in G.G.JosephKerala Mathematics: Its History and Possible Transmission to Europe, pp. 181–202. Delhi: B.R. Publishing Corporation., (1983) An Introduction to the History of Mathematics,(5th edition. Philadelphia: Saunders.Fauvel, J. and J.Gray, (eds) (1987) The History of Mathematics: A Reader. London: Macmillan.1986) ‘Brook Taylor and the Method of Increments’, Archive for the History of Exact Sciences, 34(1): 1–140. http://dx.doi.org/10.1007/BF00329903(1928) ‘The Source of the so-called Pellian Equations’, Bulletin of the Calcutta Mathematical Society, 19: 151–76.(2003) ‘Mathematics and Modesty in the Society of Jesus: The Problems of Christoph Grienberger (1564–1636)’, in MordechaiFeingold (ed.), The New Science and Jesuit Science: Seventeenth Century Perspectives, Archimedes vol. 6. pp. 1–120. Kluwer: Dordrecht.(1955) Malayala Bhasha Charitram. Kottayam: National Book Stall.(1969) ‘Second Order Interpolation in Indian Mathematics up to the Fifteenth Century’, Indian Journal of History of Science, 4 (1&2): 86–98.(1860) Day Dawn in Travancore. Kottayam: CMS Press.(1995) The Bhakhshali Manuscript: An Ancient Mathematical Treatise. Groningen: Egbert Forsten.(1990) ‘The Correction of the Madhava Series for the Circumference of a Circle’, Centaurus, 33 (2&3): 149–74. http://dx.doi.org/10.1111/j.1600-0498.1990.tb00725.x, and , (1910) ‘Diophantus’ Method of Solution’, in Diophantus of Alexandria: A Study in the History of Greek Algebra. Cambridge: Cambridge University Press.(2007) The Tacit Appropriation of Hindu Algebra in Renaissance Practical Arithmetic. Belgium: Centre for Logic and Philosphy of Science, Ghent University.(1983) Selected Studies in History of Science, Coimbra: Por ordem da Universidade Coimbra.(1998) Johann Schreck Terrentius. Napoli: Instituto Universitario Orientale.(2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer. New York: Wiley.(1988) ‘Western Influence and Chinese Tradition in an Eighteenth Century Chinese Mathematical Work’, Historia Mathematica, 15: 311–31. http://dx.doi.org/10.1016/0315-0860%2888%2990024-9(1999) Squaring the Circle: The War between Hobbes and Wallis. Chicago: University of Chicago Press.(1994a) ‘Different Ways of Knowing: Contrasting Styles of Argument in Indian and Greek Mathematical Traditions’, in Ernest (ed.), Mathematics, Education and Philosophy: An International Perspective, pp. 194–204. London: The Falmer Press.(1994b) ‘Tibetan Astronomy and Mathematics’, in I.Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy 7 of the Mathematical Sciences, pp. 131–36. London: Routledge.(1995) ‘Cognitive Encounters in India during the Age of Imperialism’, Race and Class, 36(3): 39–56. http://dx.doi.org/10.1177/030639689503600303(1997) ‘What is a Square Root? A Geometrical Representation in Different Mathematical Traditions’, Mathematics in Schools, 23(3), 4–9, reprinted in C.Pritchard (ed.), The Changing Shape of Geometry. Cambridge: Cambridge University Press, 2003.(2000) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton and London: Princeton University Press.(Joseph, G.G. (ed.) (2009) Kerala Mathematics: Its History and Possible Transmission to Europe. Delhi: B.R. Publishing Corporation.1964) Geschichte der Matematik im Mittelater, German translation. Leipzig.(1992) A History of Mathematics: An Introduction. New York: Harper Collins.(1908) ‘Notes on Indian Mathematics’, Journal of the Asiatic Society of Bengal, 4: 111–41.(Expounding the Mathematical Seed: A Translation of Bhaskara I on the Mathematical Chapter of Aryabhatiya, Vol 1. Basel: Birkauser Verlag.1972) Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.(1963) ‘Astronomy and Mathematics in Kerala’, Adyar Library Bulletin, 27: 118–67.(1985) Vedanga Jyotisa of Lagadha in its RK and Yajur Recensions. Delhi: Indian National Science Academy.(1986) ‘The Conceptual Origins of Our Numeral System and the Symbolic Form of Algebra’, Archive for History of Exact Sciences, 36: 183–99. http://dx.doi.org/10.1007/BF00412260. (1987) ‘Linkages: Exploring the Similarities between the Chinese Rod Numeral System and Our Numeral System’, Archive for History of Exact Sciences, 37: 365–92.. (1906) Malabar, 2 vols. Trivandrum: Charithram Publications.(1987) Chinese Mathematics: A Concise History. Oxford: Clarendon Press.and (1991) ‘Origins of Katapayadi System of Numerals’, Sri Rama Varma Samskrta Granthavali Journal, 18(2): 35–48.(1912) ‘Aryabhata's Rule in Relation to Indeterminate Equations of the First Degree’, Bulletin of the Calcutta Mathematical Society, 3: 11–12.(2002) ‘Geometrical Approach to Arithmetic Progressions from Nilakantha's Aryabhatiyabhasya and Sankara's Kriyakramakari’, proceedings of the International Seminar and Colloquium on 1500 Years of Aryabhateeyam, Kerala Sastra Sahitya Parishad, Kochi, pp. 143–47.(2004) ‘An Interesting Algorithm for Computation of Sine Tables from the Golasara of Nilaka(ha’, Ganita Bharati, 26: 40–55.
2009) Trignometric Sines and Sine Tables in India: A Survey. A Preprint, AHRB Project, University of Manchester.(2009a) ‘Indian Mathematical Tradition: The Kerala Dimension’, in G.G.Joseph (ed.), Medieval Kerala Mathematics: History and Its Possible Transmission to Europe, pp. 35–58. Delhi: B.R. Publishing Corporation.and (2009b) ‘Kerala Mathematics: Motivation, Rationale and Method’, in G.G.Joseph (ed.), Medieval Kerala Mathematics: History and Its Possible Transmission to Europe, pp. 77–112. Delhi: B.R. Publishing Corporation.and (1944) ‘On the Hindu Quadrature of the Circle’, Journal of the Bombay Branch of the Royal Asiatic Society, (NS) 20: 65–82.and (1931) Laghu Ramayana, Tuncattu Granthavali, No. 3, Chittoor.(1952–1953) ‘Tuncattu Ezhuttacchan’, Tuncattu Ezhuttacchan Monthly, III(3): 127–35.(1979) Social and Cultural History of Kerala. New Delhi: Sterling Publisher.(1951) Kerala Bhasha Sahitya Charitram, 7 vols. Trivandrum: Vidyavilasini Book Depot.(1983), ‘A History of the Nambudiri Community in Kerala’, in F.Staal (ed.), Agni, vol. II. Berkeley: Asian Humanities Press.and (1975) Kara(amrta of Citrabhanu, Trivandrum Sanskrit series. No. 240, Trivandrum: University of Kerala.
1959) Science and Civilization in China. Vol 3. Cambridge: Cambridge University Press.(1969) The Grand Titration: Science and Society East and West. London: Allen and Unwin.(1962) The Exact Sciences in Antiquity. New York: Harper.(1948) How Greek Science Passed to the Arabs. London: Routledge and Keegan Paul.(1849) ‘Arithmetic—including a History of the Science’, in Encylcopedia Metropolitana or Universal Dictionary of Knowledge; Part 6, First Division. London: J J Griffin and Co.(1957) Aryabha(ya bha
ya of Nīlakantha, Golapada, Trivandrum Sanskrit series No. 185. Trivandrum: University of Kerala.
2001) ‘The “Error” in the Indian “Taylor Series Approximation” to the Sine’, Historia Mathematica, 28: 283–95. http://dx.doi.org/10.1006/hmat.2001.2331(1939) ‘On James Gregory's Geometriae Pars Universalis’, in H.W.Turnball (ed.) James Gregory Tercentenary Memorial Volume. Containing His Correspondence with John Collins and His Hitherto Unpublished Mathematical Manuscripts, Together with Addresses and Essays Communicated to the Royal Society of Edinburgh. London: G. Bell & Sons.(2002) ‘Swarupam: An Introductory Essay’, in ChampakalakshmiR et al. (eds), State and Society in Pre-modern South India, pp. 120–30. Trissur: Cosmobooks.(2009) ‘Uncatalogued Malayalam Manuscripts in Europe: A Report of Work Carried out in Two Libraries in Rome, in G.G.Joseph, (ed.), Kerala Mathematics: Its History and Possible Transmission to Europe, pp. 77–112. Delhi: B.R. Publishing Corporation.(1963) ‘Astronomy and Mathematics in Kerala’, Adyar Library Bulletin, 27: 118–67.(1944), ‘On the Hindu Quadrature of the Circle’, Journal of the Royal Asiatic Society (Bombay branch), 20: 65–82.and (1949) ‘The Sine and Cosine Power Series in Hindu Mathematics’, Journal of the Royal Asiatic Society of Bengal, 15: 1–13.and (1951) ‘On the Hindu Proof of Gregory's Series’, Scripta Mathematica, 17: 65–74.and (1952) ‘On the Hindu Proof of Gregory's Series’, Scripta Mathematica, 18: 65–74.and (1978) ‘On an Untapped Source of Medieval Keralese Mathematics’, Archive for the History of Exact Sciences, 18(2): 89–102.and (1986) ‘On Medieval Keralese Mathematics’, Archive for the History of Exact Sciences, 35(2): 91–99. http://dx.doi.org/10.1007/BF00357622and (2002) ‘Aryabhateeyam in the Light of Aryabhateeyam-bhashya by Nilakantha Somayaji’, proceedings of the International Seminar and Colloquium on 1500 Years of Aryabhateeyam, Kerala Sastra Sahitya Parishad, Kochi, pp. 115–22.(1994) ‘Heliocentric Model of Planetary Motion in the Kerala School of Indian Astronomy’, Current Science, 66: 784–90., and (1952) Yuktibha, (a, Part I. Trichur: Mangalodayam.
1994) ‘Indian Mathematics in Arabic’, in Ch.Sasaki, J.W.Dauben, M.Sugiura (eds), The Intersection of History and Mathematics. pp. 143–48. Basel, Boston and Berlin: Birkhaüser Verlag. http://dx.doi.org/10.1007/978-3-0348-7521-9(1879) ‘Lecon de calcul d'Aryabhata’, Journal Asiatique, Septieme Serie, 13: 393–434.(1994) A History of Arabic Astronomy. New York: New York University Press.(1930) Āryabhatīya with bhāsya of Nīlaka(ha, Part I, Trivandrum Sanskrit series No. 101, Trivandrum.
1931) Aryabha(iya with bha
ya of Nilaka
ha, Part II, Trivandrum Sanskrit series. No. 110, Trivandrum.
1963) ‘Development of Mathematical Series in India’, Bulletin of the National Institute of Sciences (India), 21: 320–43.(1979) Geometry in Ancient and Medieval India. Delhi: Indological Publ.(1956) Venvaroha of Madhava with commentary by Acyuta Pisarati. Sanskrit College Committee, Tripunithura, Vishveshvaranand Institute.(1957) Goladipika of Paramesvara. Madras: Adayar Library.(1958) ‘Jyesthadeva and his Identification as the Author of Yuktibhasa’, Adyar LibraryBulletin, 22: 35–40.(1963) Drgganita of Paramesvara. Hoshiarpur: Vishveshavaranand Institute.(1972a) ‘Some Direct Lines of Astronomical Tradition in Kerala’, P.C.Shastry Felicitation Volume. Delhi: Chaturveda.(1972b) A History of Kerala School of Hindu Astronomy. Hoshiarpur: Vishveshavaranand Institute.(Sarma, K.V. (ed.) (1972c) Lilavati of Bhaskaracarya with Kriyakramakari of Sankara and Narayana. Hoshiarpur: Vishveshavaranand Institute.1974) Sphutanirnaya Tantra of Acyuta with Auto commentary. Hoshiarpur: Vishveshavaranand Institute.(1975) Lilavati of Bhaskaracarya with the Kriyakramakari of Sankara and Narayana. Hoshiarpur: Vishveshavaranand Institute.(1977a) Rasigolasphutaniti of Acyuta. Hoshiarpur: Vishveshavaranand Institute.(1977b) Tantrasangaha of Nilakantha Somayaji with the Yuktidipika and Laghuvivrti of Śånkara. Hoshiarpur: Vishveshavaranand Institute.(1985) Vedanga Jyotisa & Lagadha (in its R K and Yajus Recensious) (with the translational notes of Professor T.S. Kuppana Sastry). Delhi: Indian National Science Academy.(2001) Sadratnamala of Sankaravarman. Delhi: Indian National Science Academy.(2002) Science Texts in Sanskrit in the Manuscripts Repositories of Kerala and Tamilnadu. Delhi: Rashtriya Sanskrit Sansthan.(2008) GanitaYuktiBhasa of Jyesthadeva, 2 vols. New Delhi: Hindustgan Book Agency.(1964) Vakyakarana (Vakyapancaddhyayi). Madras: Kuppuswam Research Institute.and (1991) ‘Yuktibhasa of Jyesthadeva’, Indian Journal of History of Science, 26: 186–207.and . (2002) ‘Rule of Three and Its Variations in India’ in Y.Dold-SamploniusJ.W.Dauben, M.Folerts and B.van Dalen (eds), From China to Paris: 2000 Years of Transmission of Mathematical Ideas, pp. 133–56. Stuttgart: Steiner Verlag.(2003) ‘Sunya in Pingala's Chandahsutra’, in A.K.Bag and S.R.Sharma (eds), The Concept of Sunya, pp. 126–36. Delhi: Aryan Books.(2009) ‘Early Transmissions of Indian Mathematics’, in G.G.Joseph (ed.) Kerala Mathematics: Its History and Possible Transmission to Europe, pp. 35–58. Delhi: B.R. Publishing Corporation.(1981 [1938]) The Mathematical Work of John Wallis. London: Taylor and Francis.(1873) ‘The Great Autumnal Execution’, in the Bulletin of the Bibliography and History of Mathematical & Physical Sciences, published by B.Boncompagni, member of Pontific Academy, reprinted in Sources of Science, No. 10 (1964), New York and London.(1845–1849) Sciences Mathematique chez les Grecs et les Orienteaux, vol. II. Paris: Libraire de Firmin Didot Freres.(1927) ‘The Aryabhatiyam, Translated into English’, Journal of the Department of Letters, 16: 1–56.(Shukla, K.S. (ed.) (1957) The Suryasiddhanta with the Commentary of Paramesvara. Lucknow: Department of Mathematics and Astronomy.Shukla, K.S. (ed.) (1960) Mahabhaskariya, edited and translated into English with explanatory and critical notes, and comments, etc. Lucknow: Department of Mathematics and Astronomy, Lucknow University.Shukla, K.S. (ed.) (1976) Aryabhatiya of Aryabhata, with the Commentary of Bhaskara I and Somesvara. Delhi: Indian National Science Academy.1976) Aryabhatiya of Aryabhata. New Delhi: Indian National Science Academy.and (1936) ‘On the Use of Series in Hindu Mathematics’, Osiris, 1: 606–28. http://dx.doi.org/10.1086/368443(1939) ‘Hindu Trigonometry’, Proceedings of the Benares Mathematical Society, 1: 77–92.(1923/5) History of Mathematics, 2 vols. Boston, MA: Ginn & Co.)(Reprinted by Dover, New York, 1958.(1985) Indian Astronomy—A Source-Book. Bombay: Nehru Centre.and (1996), Born to Rebel. London: Little, Brown & Co.((1953–57) [1953]Kerala Sahitya Caritram,3rd edition, 5 volsTrivandrum: Kerala University series 30, University of Kerala.2003) ‘Astronomy and Mathematics in Medieval Kerala with Special Reference to the Nila Valley’, in N.V.P.Unithiri (ed.), Indian Scientific Traditions. Calicut: University of Calicut.(2002) ‘A Note on Nilakantha's Bhaysa on Aryabhitya’, proceedings of the International Seminar and Colllogquium on 1500 Years of Aryabhateeyam, Kerala Sastra Sahitya Parishad, Kochi.and (2009) ‘An Intellectual Background of Medieval Kerala with Special Reference to Mathematics and Astronomy’, in G.G.Joseph (ed.), Medieval Kerala Mathematics: History and Its Possible Transmission to Europe, pp. 59–73. Delhi: B.R. Publishing Corporation.and (1976) ‘Pell's equation in Greek and Hindu mathematics’, Russian Math Surveys, 31: 210–25. http://dx.doi.org/10.1070/RM1976v031n05ABEH004198(1983) Geometry and Algebra in Ancient Civilizations. Berlin: Springer-Verlag. http://dx.doi.org/10.1007/978-3-642-61779-9(1984) Galileo and His Sources: The Heritage of the Collegio Romano in Galileo'sScience. Princeton: Princeton University Press.(1825) Kala Sankalita: A Collection of Memoirs on the Various Modes According to which the Nations of the Southern Parts of India Divide Time. Madras: College Press.(1835) ‘On the Hindu Quadrature of the Circle and the Infinite Series of the Proportion of the Circumference to the Diameter Exhibited in the Four Sastras, the Tantrasangraham, Yukti-Bhasa, Carana Padhati, and Sadratnamala’, Transactions of the Royal Asiatic Society of Great Britain and Ireland, III(iii): 309–23.(1948) Documenta Indica, 16 volumes. Rome: Monumenta Historica Societate Iesu.(About the Author
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).
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