Studies in Indian Mathematics and Astronomy: Selected Articl

This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications,...

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This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications, reminiscences from his former students, and an analysis of his monumental contributions. Part II is a collection of important articles penned by Prof. Shukla related to various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh—which together constitute the third unpublished part of their History of Hindu Mathematics—that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work.

Given the sheer range and depth of Prof. Shukla’s scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

Front Matter ....Pages i-xxii
Front Matter ....Pages 1-1
Reminiscences of Prof. K. S. Shukla (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 3-4
Dr. Kripa Shankar Shukla, veteran historian of Hindu astronomy and mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 5-12
Obituary: Kripa Shankar Shukla (1918–2007) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 13-22
Prof. K. S. Shukla’s contribution to the study of the history of Hindu astronomy (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 23-38
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Front Matter ....Pages i-xxii
Front Matter ....Pages 1-1
Reminiscences of Prof. K. S. Shukla (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 3-4
Dr. Kripa Shankar Shukla, veteran historian of Hindu astronomy and mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 5-12
Obituary: Kripa Shankar Shukla (1918–2007) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 13-22
Prof. K. S. Shukla’s contribution to the study of the history of Hindu astronomy (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 23-38
The seminal contribution of K. S. Shukla to our understanding of Indian astronomy and mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 39-69
Front Matter ....Pages 71-71
Hindu mathematics in the seventh century as found in Bhāskara I’s commentary on the Āryabhaṭīya (I) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 73-87
Hindu mathematics in the seventh century as found in Bhāskara I’s commentary on the Āryabhaṭīya (II) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 88-106
Hindu mathematics in the seventh century as found in Bhāskara I’s commentary on the Āryabhaṭīya (III) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 107-109
Hindu mathematics in the seventh century as found in Bhāskara I’s commentary on the Āryabhaṭīya (IV) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 110-119
On Śrīdhara’s rational solution of Nx2 + 1 = y2 (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 120-132
Ācārya Jayadeva, the mathematician (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 133-152
Series with fractional number of terms (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 153-159
Hindu methods for finding factors or divisors of a number (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 160-168
Magic squares in Indian mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 169-186
Front Matter ....Pages 187-187
Hindu geometry (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 189-267
Hindu trigonometry (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 268-344
Use of calculus in Hindu mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 345-355
Use of permutations and combinations in India (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 356-376
Magic squares in India (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 377-437
Use of series in India (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 438-461
Surds in Hindu mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 462-474
Approximate values of surds in Hindu mathematics (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 475-483
Front Matter ....Pages 485-485
Astronomy in ancient and medieval India (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 487-494
Main characteristics and achievements of ancient Indian astronomy in historical perspective (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 495-509
On three stanzas from the Pañcasiddhāntikā (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 510-516
The Pañcasiddhāntikā of Varāhamihira (1) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 517-532
The Pañcasiddhāntikā of Varāhamihira (2) (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 533-547
Āryabhaṭa I’s astronomy with midnight day-reckoning (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 548-568
Glimpses from the Āryabhaṭasiddhānta (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 569-576
Front Matter ....Pages 577-577
Early Hindu methods in spherical astronomy (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 579-599
Use of hypotenuse in the computation of the equation of the centre under the epicyclic theory in the school of Āryabhaṭa I ??? (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 600-615
Hindu astronomer Vaṭeśvara and his works (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 616-624
The evection and the deficit of the equation of the centre of the Moon in Hindu astronomy (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 625-645
Phases of the Moon, rising and setting of planets and stars and their conjunctions (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 646-694
Front Matter ....Pages 695-695
Vedic Mathematics: The deceptive title of Swamiji’s book (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 697-704
A note on the Rājamṛgāṅka of Bhoja published by the Adyar Library (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 705-706
Review of Rājamṛgāṅka of Bhojarāja (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 707-708
Review of Karaṇaratna of Devācārya (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 709-714
A note on Raymond P. Mercier’s review of “Karaṇaratna of Devācārya” (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 715-718
The yuga of the Yavanajātaka: David Pingree’s text and translation reviewed (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 719-731
Review of Vaṭeśvarasiddhānta and Gola of Vaṭeśvara (Aditya Kolachana, K. Mahesh, K. Ramasubramanian)....Pages 732-733
Back Matter ....Pages 734-742
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