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Calculating the sine of one degree, not possible with the tools of geometry alone, was a problem approached frequently in various ways in Hellenistic, Arabic, Persian, and European trigonometry. This book situates the problem and the iterative techniques often used to solve it in the context of Indian trigonometry, focusing on the Sanskrit text and manuscript that form the main subject of this study: the jyacapa section of the Siddhantakaustubha of Jagannatha. This text describes the approaches of Jamshid al-Kashi and Ulugh Beg of 15th-century Samarqand, and also includes innovations produced by astronomers of Jai Singh's court in Jaipur.
This book contains translations and editions of two recensions of the manuscript's surviving prose texts, along with analyses of its mathematical content. The authors also trace the textual history of the mathematical methods in both Islamic and Sanskrit mathematical traditions.
Of timely interest to scholars in the history of early modern Islamic and Indian mathematical sciences, this book contributes an important text to the literature on the interactions between these cultures.
Clemency Montelle is Professor in the School of Mathematics and Statistics at the University of Canterbury, Christchurch, New Zealand. She has research interests in the mathematical history of several early cultures of inquiry including Mesopotamia, Greece, India, and the Islamic near east. Recently she has co-authored several books on early mathematical astronomy, including The Sanskrit Astronomical Table Text Brahmatulyasara?i Numerical Tables in Textual Scholarship (2020) with Anuj Misra and Kim Plofker, Sanskrit Astronomical Tables (2019) with Kim Plofker, and Editing and Analysing Numerical tables (2022) coedited with Benno Van Dalen and Matthieu Husson.
Kim Plofker is Associate Professor of Mathematics at Union College in Schenectady, New York. She received her doctorate from the Department of the History of Mathematics at Brown University in 1995. Her research focuses on the history of mathematics and astronomy in India and its connections with Islamic and early modern European science. Professor Plofker's books include Mathematics in India (Princeton, 2009) and (with Anuj Misra and Clemency Montelle) The Sanskrit Astronomical Table Text Brahmatulyasarini (Brill, 2021).
Glen Van Brummelen is Professor of Mathematics at Trinity Western University in Langley, BC, Canada. He is a historian of mathematical astronomy in early cultures, especially ancient Greece, medieval Islam, and medieval and Renaissance Europe. His books include The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (2009), Heavenly Mathematics (2013), Trigonometry: A Very Short Introduction (2020), and The Doctrine of Triangles: A History of Modern Trigonometry (2021). He has served twice as president of the Canadian Society for History and Philosophy of Mathematics, and has won the Mathematical Association of America's Haimo Award for Distinguished Teaching (2016) and Canada's 3M National Teaching Fellowship (2017).
Introduction: The sine of 1? and its history.- Parallel editions and translations of the jyacapa excerpt.- Mathematical notes on the jyacapa excerpt.- Al-Birjandi and his predecessors on sine 1? approximations.- Sine 1? iteration in the Sanskrit tradition.- Discussion.- Appendix A. Anonymous Arabic treatise iteration calculations.- Bibliography.
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