The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c2.1

c2.1

In the last century, and at the beginning of the present, George Thibaut and A. Bürk brought to the notice of the scholarly world the mathematical significance of two *sūtra* texts, namely the *Śulba-sūtras* by Baudhāyana and Āpastamba. These two works are manuals for the construction of various types of altars for fire-sacrifice, an ancient cult fully established in the time of the *Saṃhitās*. Their mathematical importance lies in a precise statement of the squared relationship of the two sides and the diagonal of a rectangle, the realization of the irrationality of numbers like √2, efforts to determine their approximate values, formulation of rules for combining rectilinear figures, transforming squares into rectangles, triangles, trapeziums and circles and vice versa, the use of simple fractions and approximate values of π. All these arose from the mensuration of laying altars of a fixed square area but of different shapes and filling them with a fixed number of bricks necessarily of different geometrical shapes. The Greek tradition of the development of geometry from the more ancient Egyptian mensuration, the rope-stretcher’s art, appears to have its counterpart in the scriptural tradition of the *śulba-sūtras*. That similar tradition obtained in other culture areas has become increasingly clear with advancing knowledge of the cuneiform texts and ancient Chinese mathematical sources.