Aditya Kolachana

Bio: Aditya Kolachana is an academic researcher from Indian Institute of Technology Bombay. The author has contributed to research in topics: Sanskrit literature & Astronomer. The author has an hindex of 3, co-authored 11 publications receiving 18 citations.

Magic squares in India

Abstract: A square containing an equal number of cells in each row and each column is called a magic square, when the total of numbers in the cells of each row, each column and each diagonal happens to be the same. Magic squares have been known in India from very early times. It is believed that the subject of magic squares was first taught by Lord Śiva to the magician Maṇibhadra. Magic squares are said to have magical properties and were used in various ways by the Hindus as well as the Jainas. But the mathematics involved in the construction of magic squares and other magic figures was first systematically and elaborately discussed by the mathematician Nārāyaṇa (ad 1356) in his Gaṇitakaumudī. Some of his methods were unknown in the west and were recently discovered by the efforts of several scholars. The present article, besides giving a brief history of magic squares, explains the methods given by Nārāyaṇa and other Hindu writers for the construction of magic squares of various types.

The Candrārkī of Dinakara: A Text Related to Solar and Lunar Tables:

Abstract: A set of tables devoted to the sun and the moon, titled the Candrārkī (“Related to the moon and sun”), was compiled in Sanskrit by Indian astronomer Dinakara along with a short accompanying text, i

Madhava's Multi-Pronged Approach for Obtaining the Pranakalantara

Abstract: The prāṇakalāntara, or the difference between the longitude and the corresponding right ascension, is an important astronomical parameter used in determining the ascendant (lagna), as well as the equation of time in Indian astronomy. This paper explores the different algorithms described to calculate the prāṇakalāntara in the Lagnaprakaraṇa, a hitherto unpublished manuscript attributed to Mādhava, the founder of the Kerala school of astronomy and mathematics. We also point out the interpretation of some of the algorithms in terms of epicyclic models.

Ācārya Jayadeva, the mathematician

Abstract: The object of the present paper is to invite attention of historians of science to an important Hindu algebraist, Ācārya Jayadeva, who lived and wrote in the early 11th century of the Christian era (or earlier). His name and quotations from his work on algebra are found to occur in the Sundarī, which is the name of Śrīmad Udayadivākara’s commentary on the Laghubhāskarīya of Bhāskara I (629 AD).

Determination of Ascensional Difference in Lagnaprakarana

Abstract: The ascensional difference or the cara is a fundamental astronomical concept that is crucial in determining the durations of day and night, which are a function of the observer’s latitude and the time of the year. Due to its importance, almost all astronomical texts prescribe a certain procedure for the determination of this element. The text Lagnaprakaraṇa—a hitherto unpublished manuscript attributed to Mādhava, the founder of the Kerala school of astronomy and mathematics—however discusses not one, but a number of techniques for the determination of the cara that are both interesting and innovative. The present paper aims to discuss these techniques.

On the Persian Translation of Bhāskara’s Līlāvatī by Abu’l Faiẓ Faiẓī at the Court of Akbar

Abstract: At the court of Akbar, several Sanskrit texts were rendered into Persian; these included the epics Mahābhārata and Rāmāyaṇa, collections of fables and legends like the Pañcatantra, the Siṃhāsana-dvātriṃśikā and the Kathāsaritsāgara, and the historical work Rājataraṅgiṇī. Besides these, a Sanskrit mathematical text, the Līlāvatī of Bhāskarācārya was also translated into Persian by Akbar’s Poet Laureate Faiẓī. While the Persian translations of the Mahābhārata and others have been critically examined in modern times, the Persian version of the Līlāvatī did not receive any scholarly attention, except in two minor cases. In 1816, John Taylor, in the preface to his translation of the Līlāvatī from the Sanskrit, opined that Faiẓī’s Persian version omits certain sections of the Līlāvatī. In 1952, H. J. J. Winter and Arshad Mirza discussed a small fragment of the Persian version and translated 10 verses from it into English. Therefore, in this paper, an attempt is made for the first time to compare the Persian version with the Sanskrit original and to critically analyse the structure and style of the Persian version.

Music Theory, Mathematics, and Patterns of Innovation in the Saṅgītaratnākara

Abstract: Abstract This paper investigates the relationship between textuality and mathematics in the Saṅgītaratnākara, a Sanskrit work on music composed in the thirteenth century by Śārṅgadeva. Within the traditional Sanskrit knowledge system on musicology, the Saṅgītaratnākara can be regarded as a seminal work, given the commentaries it has inspired and the innovative features it contains. I shall explore some textual aspects which, in Medieval India, have contributed to establish the authority of this text and whose significance can be traced in later works. Among these are types of verbalization and mathematical procedures whose role, I shall argue, is entirely theoretical. In the Saṅgītaratnākara, calculations and diagrams underline an innovative language of musical speculation, as well as the relationship between theory and practice and the shaping influence of other śāstric traditions. The set of conventions which are based on a vocabulary and methods shared with other technical literatures, particularly prosody and mathematics, attests the variety of literary practices introduced by Śārṅgadeva. I shall argue that this text builds up a code whose aim and function are not necessarily musicological in character. Although orality clearly retains its special status as the archetype of learning, Śārṅgadeva’s contribution manifests the autonomy of literature on saṅgīta as an “art” which constitutes an independent sphere of activity, defining its own rules, and adhering to its own criteria of value.

The Kriyākramakarī’s Integrative Approach to Mathematical Knowledge

Abstract: The purpose of this paper is to review the general organization of knowledge in the Kriyākramakarī, a sixteenth-century treatise of Kerala mathematics. Specifically, I will argue that the authors' interest in justification or proof is integrative, rather than hierarchical or cumulative. In other words, the purpose of proofs in the Kriyākramakarī is to connect various different aspects of mathematics, rather than just establish results by means of previously known results.

Determination of Ascensional Difference in Lagnaprakarana

Abstract: The ascensional difference or the cara is a fundamental astronomical concept that is crucial in determining the durations of day and night, which are a function of the observer’s latitude and the time of the year. Due to its importance, almost all astronomical texts prescribe a certain procedure for the determination of this element. The text Lagnaprakaraṇa—a hitherto unpublished manuscript attributed to Mādhava, the founder of the Kerala school of astronomy and mathematics—however discusses not one, but a number of techniques for the determination of the cara that are both interesting and innovative. The present paper aims to discuss these techniques.