Bhāskara-prabhā

K. RAMASUBRAMANIAN is a professor at the Cell for the Indian Science and Technology in Sanskrit, Department of Humanities and Social Sciences, Indian Institute of Technology Bombay, India. He holds a doctorate degree in Theoretical Physics, a master’s degree in Sanskrit, and a bachelor’s degree in Engineering—a weird but formidable combination of subjects to do multi-disciplinary research. He was honoured with the coveted title “Vidvat Pravara” by the Shankaracharya of Sri Sringeri Sharada Peetham, Karnataka, India, for completing a rigorous course in Advaita Vedānta (a 14-semester program), in 2003. He is one of the authors who prepared detailed explanatory notes of the celebrated works Gaṇita-yuktibhāṣā (rationales in mathematical astronomy), Tantrasaṅgraha and Karaṇa-paddhati, which bring out the seminal contributions of the Kerala School of Astronomers and Mathematicians. He was conferred the prestigious award of theMahaṛṣi Bādarāyaṇa Vyas Samman by the then President of India, in 2008, and the R. C. Gupta Endowment Lecture Award by the National Academy of Sciences India, in 2010. He is a recipient of several other awards and coveted titles as well. From 2013, he serves as an elected council member of the International Union of History and Philosophy of Science and Technology. He is also a member of various other national and international bodies. TAKAO HAYASHI is an emeritus professor of history of science from Doshisha University, Japan. He worked on the Bakhshali manuscript to obtain his PhD from Brown University in 1985. He focused on Indian mathematics history, and specifically the Bakhshali manuscript, the oldest surviving Indian text on mathematics. He was a fellow of the Japan Society for the Promotion of Science. He is a recipient of the Salomon Reinach Foundation Prize from French Institute (2001), Publication Prize from Mathematical Society of Japan (2005), and Kuwabara Prize fromthe History of Mathematics Society of Japan (2005). He is a member of American Mathematics Society, the Indian Society for History of Mathematics, the History of Science Society of Japan, and the Japanese Association of Indian and Buddhist Studies. CLEMENCY MONTELLE is an associate professor at the Department of Mathematics and Statistics, University of Canterbury, New Zealand. She earned her PhD in the History of Mathematics from Brown University, in 2005. She is the joint director of History of Mathematical Sciences in India (HAMSI), a research hub devoted to the study of the astral sciences on the Indian subcontinent. Her research interest lies in the history of mathematics.

Chapter 1. Caṅgadeva’s inscription of 1207.- Chapter 2. The legend of Līlāvatī.- Chapter 3. The poetical face of the mathematical and astronomical works of Bhāskarācārya.- Chapter 4. The līlā of the Līlāvatī.- Chapter 5. Gaṇeśa Daivajña’s upapattis for some rules in the Līlāvatī.- Chapter 6. A study of two Malayalam commentaries on the Līlāvatī.- Chapter 7. Mensuration of quadrilaterals in the Līlāvatī.- Chapter 8. Aṅkapāśa in the Līlāvatī.- Chapter 9. The Bījagaṇita of Bhāskarācārya: Some highlights.- Chapter 10. A critical study of algorithms in the Karaṇīṣaḍvidham.- Chapter 11. Grahagaṇitādhyāya of Bhāskarācārya’s Siddhāntaśiromaṇi.- Chapter 12. Bhāskarācārya and Kṣayamāsa.- Chapter 13. The Vāsanābhāṣyasof Bhāskarācārya.- Chapter 14. The production of Sines: Bhāskarācārya’s Jyotpatti.- Chapter 15. An application of the addition and subtraction formula for the Sine in Indian astronomy.- Chapter 16. Astronomical instruments in Bhāskarācārya’s Siddhāntaśiromaṇi.- Chapter 17. Bhojarājā and Bhāskara: Precursors of Karaṇakutūhala algebraic approximation formulas in the Rājamṛgāṅka.- Chapter 18. Persian translations of Bhāskara’s Sanskrit texts and their impact in the following centuries.- Chapter 19. The use of Bhūtasaṅkhyās in the Līlāvatī of Bhāskarācārya.- Chapter 20. Implications of Bhāskarācārya’s Līlāvatī to the Common Core State Standards in Mathematics.