Indian Mathematics c7.41

c7.41

The presence of a number of incorrect rules side by side with correct ones is significant. The one relating to the area of triangles and quadrilaterals, *viz.*, the area is equal to the product of half the sums of pairs of opposite sides, strangely enough occurs in a Chinese work of the 6th century as well as in the works of Ahmes, Brahmagupta, Mahāvīra, Boethius and Bede. By Mahāvīra, the idea on which it is based—that the area is a function of the perimeter—is further emphasized. Āryabhaṭa gives an incorrect rule for the volume of a pyramid; incorrect rules for the volume of a sphere are common to Āryabhaṭa, Śrīdhara and Mahāvīra. For cones all the rules assume that π=3. Mahāvīra gives incorrect rules for the circumference and area of an ellipse and so on.