Abstract
Indian Astronomy is rich in algorithms. The algorithms presented in the Indian astronomical texts have varying degrees of complexities starting from the simple trairāśika rule, to the treatment of parallax in a solar eclipse or the computation of the elevation of lunar cusps. In the present article we will discuss a few algorithms that are representative of the ingenuity and continuity of the Indian astronomical tradition. We start with the interpolation formula presented by Brahmagupta (c.665 AD) and then proceed to describe a select few algorithms from Tantrasaṅgraha of Nīlakaṇṭha composed in 1500 AD. Here we present the algorithm for the calculation of time from shadow measurements and the exact algorithm for the computation of lagna and the time for the duration of an eclipse. We also comment on the iterative process known as aviśeṣakarma which aims at circumventing the problem of interdependencies among several variables.
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References
Donald E. Knuth, The Art of Computer Programming, Vol. 1, Addison Wesley, 1973, p 1–2.
C.B. Boyer, A History of Mathematics, John Wiley and Sons, 1989, p 256.
See for instance, 500 years of Tantrasangraha : A Landmark in the History of Astronomy, Ed. by M.S. Sriram, K. Ramasubramanian and M.D. Srinivas, Indian Institute of Advanced Study, Shimla, 2002.
(i) The verses attributed to Mādhava (c.l4th century) by Sankara Vāriyar in his commentary to Tantrasangraha (Chap 2, verses 437, 438) beginning with and for obtaining the sine and cosine values for ANY DESIRED ANGLE, yield results correct up to 7 decimal places. This is indeed a remarkable result which may be considered far ahead of his times, (ii) For more details and mathematical exposition of the above the reader may refer to the article by M.S. Sriram published in the present volume.
Līlāvatī of Bhāskarācārya with the commentary of Śankara and Nārāyana, Ed. by K.V. Sarma, VVRI, Hoshiarpur, 1975, ver.73, p 178.
Ganita-yuktibhāsā, Ed. with English Translation by K.V. Sarma, with Explanatory Notes by K.Ramasubramanian, M.D. Srinivas and M.S. Sriram (in press), Vol. I, Chap 4.
Khaṅdakhādyaka of Brahmagupta, Ed. and Tr. by Bina Chat-terjee, Motilal Banarsidass, 1970, Vol. 2, Uttarakhaṅdakhādyaka, Chap 1, ver.4.
Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 1983, p 774.
See for instance, Siddhantasiromani, Chap 3, verses 12–14.
For a detailed exposition on this, see K. Ramasubramanian and M.S. Sriram, Corrections to the terrestrial latitude in Tantrasangraha, Indian Journal of History of Science, 38.2, 2003, p 129–144.
Tantrasangraha of Nilakantha with the prose commentary Laghuvivrtti of Sankara Vāriyar, Ed. by Surnad Kunjan Pillai, Trivandrum Sanskrit Series no. 188, Trivandrum 1958, Chapter 3, verses 23–25.
ibid., verses 19–21.
ibid., verses 95–100.
ibid., verses 100–101.
ibid., verse 102.
ibid., verses 104–105.
ibid., verses 107–109.
ibid., Chapter 2, verses 53–54.
Tantrasangraha of Nilakantha with Yuktidīpikā, commentary in the form of verses by Śahkara Vāriyar, Ed. by K.V. Sarma, VVBIS, Punjab University, 1977, Chap 4, verses 79 and 87, p 261–62.
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Ramasubramanian, K. (2005). Algorithms in Indian Astronomy. In: Emch, G.G., Sridharan, R., Srinivas, M.D. (eds) Contributions to the History of Indian Mathematics. Culture and History of Mathematics, vol 3. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-25-5_8
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DOI: https://doi.org/10.1007/978-93-86279-25-5_8
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