Gaṇitānanda: Selected Works of Radha Charan Gupta on History of Mathematics

Description

This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses. Front Matter ....Pages i-xxvii Front Matter ....Pages 1-1 A Portrait of the Life of R. C. Gupta (K. Ramasubramanian)....Pages 3-8 A Birthday Tribute to R. C. Gupta (Christoph J. Scriba)....Pages 9-12 Professor R. C. Gupta Receives the Kenneth O. May Prize (Kim Plofker)....Pages 13-15 Front Matter ....Pages 17-17 On the Date of Śrīdhara (K. Ramasubramanian)....Pages 19-21 In the Name of Vedic Mathematics (K. Ramasubramanian)....Pages 23-26 Foreign Reviews and Evaluation of Indian Works on History of Science (K. Ramasubramanian)....Pages 27-30 The Study of History of Mathematical Sciences in India (K. Ramasubramanian)....Pages 31-40 Historical Notes: Kali Chronograms of Nārāyaṇa Bhaṭṭatiri (K. Ramasubramanian)....Pages 41-44 Front Matter ....Pages 45-45 On Some Mathematical Rules from the Āryabhaṭīya (K. Ramasubramanian)....Pages 47-54 Decimal Denominational Terms in Ancient and Medieval India (K. Ramasubramanian)....Pages 55-61 New Indian Values of \(\pi \) from the Mānava-śulba-sūtra (K. Ramasubramanian)....Pages 63-72 The Lakṣa Scale of the Vālmīki Rāmāyaṇa and Rāmā’s Army (K. Ramasubramanian)....Pages 73-79 The Chronic Problem of Ancient Indian Chronology (K. Ramasubramanian)....Pages 81-88 A Problem on Interest in the Nārada-purāṇa (K. Ramasubramanian)....Pages 89-91 Who Invented the Zero? (K. Ramasubramanian)....Pages 93-107 World’s Longest Lists of Decuple Terms (K. Ramasubramanian)....Pages 109-115 Front Matter ....Pages 117-117 Circumference of the Jambūdvīpa in Jaina Cosmography (K. Ramasubramanian)....Pages 119-128 Mādhavacandra’s and Other Octagonal Derivations of the Jaina Value \(\pi = \sqrt{10}\) (K. Ramasubramanian)....Pages 129-138 Chords and Areas of Jambūdvīpa Regions in Jaina Cosmography (K. Ramasubramanian)....Pages 139-142 The First Unenumerable Number in Jaina Mathematics (K. Ramasubramanian)....Pages 143-158 गोलपृष्ठ के लिये महावीर-फेरू सूत्र और विदेशों में उनकी झलक (K. Ramasubramanian)....Pages 159-167 Front Matter ....Pages 169-169 Brahmagupta’s Formulas for the Area and Diagonals of a Cyclic Quadrilateral (K. Ramasubramanian)....Pages 171-175 On the Volume of a Sphere in Ancient India (K. Ramasubramanian)....Pages 177-189 Kamalākara’s Mathematics and Construction of Kuṇḍas (K. Ramasubramanian)....Pages 191-211 Area of a Bow-Figure in India (K. Ramasubramanian)....Pages 213-225 Yantras or Mystic Diagrams: A Wide Area for Study in Ancient and Medieval Indian Mathematics (K. Ramasubramanian)....Pages 227-260 Front Matter ....Pages 1-1 Second-Order Interpolation in Indian Mathematics up to the Fifteenth Century (K. Ramasubramanian)....Pages 263-276 Munīśvara’s Modification of Brahmagupta’s Rule for Second-Order Interpolation (K. Ramasubramanian)....Pages 277-283 Varāhamihira’s Calculation of \(^nC_r\) and the Discovery of Pascal’s Triangle (K. Ramasubramanian)....Pages 285-289 The Last Combinatorial Problem in Bhāskara’s Līlāvatī (K. Ramasubramanian)....Pages 291-297 Early Pandiagonal Magic Squares in India (K. Ramasubramanian)....Pages 299-312 Front Matter ....Pages 313-313 Bhāskara I’s Approximation to Sine (K. Ramasubramanian)....Pages 315-331 Fractional Parts of Āryabhaṭa’s Sines and Certain Rules Found in Govindasvāmin’s Bhāṣya on the Mahābhāskarīya (K. Ramasubramanian)....Pages 333-343 Early Indians on Second-Order Sine-Differences (K. Ramasubramanian)....Pages 345-351 An Indian Form of Third-Order Taylor Series Approximation of the Sine (K. Ramasubramanian)....Pages 353-355 Solution of the Astronomical Triangle as Found in the Tantrasaṅgraha (AD 1500) (K. Ramasubramanian)....Pages 357-369 Addition and Subtraction Theorems for the Sine and the Cosine in Medieval India (K. Ramasubramanian)....Pages 371-387 Parameśvara’s Rule for the Circum-radius of a Cyclic Quadrilateral (K. Ramasubramanian)....Pages 389-395 Indian Values of the Sinus Totus (K. Ramasubramanian)....Pages 397-415 South Indian Achievements in Medieval Mathematics (K. Ramasubramanian)....Pages 417-442 Munīśvara’s Traditional Sine Table (K. Ramasubramanian)....Pages 443-449 Front Matter ....Pages 451-451 Prabodh Chandra Sengupta (1876–1962): Historian of Indian Astronomy and Mathematics (K. Ramasubramanian)....Pages 453-457 Bibhutibhusan Datta (1888–1958): Historian of Indian Mathematics (K. Ramasubramanian)....Pages 459-465 Review of Pingree’s Census of Exact Sciences in Sanskrit (1992) (K. Ramasubramanian)....Pages 467-470 Homage to Professor Abraham Seidenberg (1916–1988) (K. Ramasubramanian)....Pages 471-473 Sudhākara Dvivedī (1855–1910): Historian of Indian Astronomy and Mathematics (K. Ramasubramanian)....Pages 475-487 Clas-Olof Selenius (1922–1991): An Expert in Indian Cyclic Method (K. Ramasubramanian)....Pages 489-493 Kripa Shankar Shukla (1918–2007): Veteran Historian of Hindu Astronomy and Mathematics (K. Ramasubramanian)....Pages 495-501 Obituary—T. A. Sarasvati Amma (K. Ramasubramanian)....Pages 503-506 The India-Born First President of the London Mathematical Society and His Discovery of Ramachandra (K. Ramasubramanian)....Pages 507-516 M. Rangacharya and His Century Old Translation of the Gaṇita-sāra-saṅgraha (K. Ramasubramanian)....Pages 517-521 Front Matter ....Pages 523-523 Indian Astronomy and Mathematics in the Eleventh-Century Spain (K. Ramasubramanian)....Pages 525-529 Indian Astronomy in West Asia (K. Ramasubramanian)....Pages 531-539 Spread and Triumph of Indian Numerals (K. Ramasubramanian)....Pages 541-554 Indian Mathematical Sciences Abroad During Pre-modern Times (K. Ramasubramanian)....Pages 555-561 Sino-Indian Interaction and the Great Chinese Buddhist Astronomer-Mathematician I-Hsing (ad 683–727) (K. Ramasubramanian)....Pages 563-574 Indian Mathematical Sciences in Ancient and Medieval China (K. Ramasubramanian)....Pages 575-604 Indian Influence on Early Arabic and Persian Writers of Mathematical Sciences (K. Ramasubramanian)....Pages 605-611 Back Matter ....Pages 613-639