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An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere
While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.
Archimedes, Bhaskara, Pedagogy, Sphere, Surface Area, Volume.
- Sudhakara Dvivedi, editor. Mahāsiddhānta of Āryabhaṭa. Brajbhushan Das & Co., Benaras, 1910.
- Kedaradatta Joshi, editor. Siddāntaśiromaṇeḥ golādhyāyaḥ. Motilal Banarasidas, New Delhi, 1988.
- K. S. Shukla and K. V. Sarma, editors. Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara. Indian National Science Academy, New Delhi, 1976.
- Sudhakara Dvivedi, editor and commentator. Brahmasphuṭasiddānta and Dhyānagrahopadeśādhyāya by Brahmagupta. 1902. Reprint from The Pandit, Journal of Government Sanskrit College.
- Bina Chatterjee. Śiṣyadhīvṛddhidatantra of Lalla, Volume I. Indian National Science Academy, New Delhi, 1981.
- Sudyumnacharya, editor and translator. Triśatikā of Śrīdhara. Rashtriya Sanskrit Sansthan, New Delhi, 2004.
- R. C. Gupta. On the Date of Śrīdhara. In: Gaṇita Bhāratī. 9(1-4):54–56, 1987.
- L.C. Jain, editor. Mahāvīrāchārya’s Gaṇitasārasaṁgraha. Jaina Saṁskṛti Saṁrakshaka Saṁgha, Sholapur, 1963.
- R. C. Gupta. Mahāvīra-pheru Forumula for the Surface of a Sphere and some other Empirical Rules. Indian Journal of History of Science, 46(4):639–657, 2011.
- K. V. Sarma, editor. Līlāvatī of Bhāskarācārya with Kriyākramakarī. Vishveshvaranand Institute Publication, Hoshiarpur, 1975.
- Dattatreya Apte, editor. Līlāvatī of Bhāskara with Buddhivilāsinī and Vivaraṇa, Volume II. Ānandāśrama Sanskrit Book Series, 1937.
- Satyadeva Sharma. Siddāntaśiromaṇi with Sūryaprabhā Hindi Commentary. Chaukhamba Surabharati Prakashan, Varanasi, 2007.
- Thomas L. Heath. The Method of Archimedes. Cambridge University Press, 1912.
- Asger Aaboe. Episodes from The Early History of Mathematics, Volume 13. The Mathematical Association of America, 1st edition, 1964.
- Thomas L. Heath. The Works Of Archimedes. Cambridge University Press, 1897.
- Reviel Netz. The Works of Archimedes, Volume I. Cambridge University Press, 2010.
- C. H. Edwards Jr. The Historical Development of the Calculus. Springer-Verlag, New York, 1937.
- Larry J. Gerstein. Introduction to Mathematical Structures and Proofs. Springer-Verlag, New York, 1996.
- R. C. Gupta. Bhāskara II’s Derivation for the Surface of a Sphere. The Mathematics Education, 7:49–52, 1973.
- Takao Hayashi. Calculations of the Surface of a Sphere in India. The Science and Engineering Review of Doshisha University, 37(4):194–238, 1997.
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