From Samarqand to Jaipur

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 Brahmatulyasāraṇī 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 jyācāpa excerpt.- Mathematical notes on the jyācāpa excerpt.- Al-Bīrjandī and his predecessors on sine 1◦ approximations.- Sine 1◦ iteration in the Sanskrit tradition.- Discussion.- Appendix A. Anonymous Arabic treatise iteration calculations.- Bibliography.