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Measurement of volumes in the Gaṇita-Sāra-Saṅgraha of Mahāvīrācārya (c.850 AD)

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Author Affiliations

  • 1Department of Mathematics, Government First Grade College, Yelahanka, Bangalore-560 064, India
  • 2Department of Mathematics, Government First Grade College, , Vijayanagara, Bangalore-560 104, India

Res. J. Recent Sci., Volume 15, Issue (3), Pages 115-118, July,2 (2026)

Abstract

Ancient Indian mathematical texts presented detailed problems in arithmetic, algebra, and geometry, which were essential for daily life. Mahāvīrācārya’s treatise, the Gaṇita-Sāra-Saṅgraha (GSS), represents a significant contribution to mathematics. This work comprises nine chapters and approximately 1100 verses. Chapter eight, titled Khātavyavahāraḥ (Calculations regarding excavations), uniquely and thoroughly addresses calculations for the depth of a ditch, the volume of a pyramid and its frustum, the volume of a cone, and the volume of a sphere. He developed formulas for calculating the areas and volumes of both regular and irregular polygons. His contributions represent a significant and distinctive advancement upon the work of earlier mathematicians such as Āryabhaṭa and Bramhagupta. This paper examines issues concerning certain calculations and other Indian mathematical texts, offering modern mathematical interpretations.

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