An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere

Authors

  • K. Mahesh
  • Aditya Kolachana
  • K. Ramasubramanian

DOI:

https://doi.org/10.18311/jims/2018/18897

Keywords:

Archimedes, Bhāskara, Pedagogy, Sphere, Surface area, Volume.

Abstract

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 SiddhāntaÅ›iromaṇi (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.

Downloads

Download data is not yet available.

Author Biographies

K. Mahesh

IIT Bombay

Aditya Kolachana

IIT Bombay

K. Ramasubramanian

IIT Bombay

References

Sudhakara Dvivedi, editor. Mahćsiddhćnta of ć€ryabhaá¹­a. Brajbhushan Das & Co., Benaras, 1910.

Kedaradatta Joshi, editor. SiddćntaÅ›iromaṇeḥ golćdhyćyaḥ. Motilal Banarasidas, New Delhi, 1988.

K. S. Shukla and K. V. Sarma, editors. ć€ryabhaá¹­ć«ya of ć€ryabhaá¹­a with the commentary of Bhćskara I and SomeÅ›vara. Indian National Science Academy, New Delhi, 1976.

Sudhakara Dvivedi, editor and commentator. Brahmasphuá¹­asiddćnta and DhyćnagrahopadeÅ›ćdhyćya by Brahmagupta. 1902. Reprint from The Pandit, Journal of Government Sanskrit College.

Bina Chatterjee. Åšiá¹£yadhć«vá¹›ddhidatantra of Lalla, Volume I. Indian National Science Academy, New Delhi, 1981.

Sudyumnacharya, editor and translator. TriÅ›atikć of Åšrć«dhara. Rashtriya Sanskrit Sansthan, New Delhi, 2004.

R. C. Gupta. On the Date of Åšrć«dhara. In: Gaṇita Bhćratć«. 9(1-4):54–56, 1987.

L.C. Jain, editor. Mahćvć«rćchćrya's Gaṇitasćrasaṁgraha. Jaina Saá¹ská¹›ti Saá¹rakshaka Saá¹gha, Sholapur, 1963.

R. C. Gupta. Mahćvć«ra-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. Lć«lćvatć« of Bhćskarćcćrya with Kriyćkramakarć«. Vishveshvaranand Institute Publication, Hoshiarpur, 1975.

Dattatreya Apte, editor. Lć«lćvatć« of Bhćskara with Buddhivilćsinć« and Vivaraṇa, Volume II. ć€nandćÅ›rama Sanskrit Book Series, 1937.

Satyadeva Sharma. SiddćntaÅ›iromaṇi with SÅ«ryaprabhć 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. Bhćskara 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.

Published

2018-01-04

How to Cite

Mahesh, K., Kolachana, A., & Ramasubramanian, K. (2018). An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere. The Journal of the Indian Mathematical Society, 85(1-2), 139–169. https://doi.org/10.18311/jims/2018/18897