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Baudhayana (fl. c. 800 BCE) was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sutraappendices to the Vedas giving rules for the construction of altarscalled the Baudhayana Sulbasūtra, which contained several important mathematical results. He is older than other famous mathematician Apastambha. He belongs to Yajurveda school. 

He is accredited with calculating the value of π to some degree of precision, and with discovering what is now known as the Pythagorean theorem. Another problem tackled by Baudhayana is that of finding a circle whose area is the same as that of a square (the reverse of squaring the circle). Baudhayana gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2. An interesting, and quite accurate, approximate value for √2 is given in Chapter 1 verse 61 of Baudhayana's Sulbasutra. The Sanskrit text gives in words what we would write in symbols as


√2 = 1 + 1/3 + 1/ (3×4)  1/ (3×4×34) = 577/408


which is, to nine places, 1.414215686. This gives √2 correct to five decimal places. 

The Sulbasutra of Baudhayana contains geometric solutions (but not algebraic ones) of a linear equation in a single unknown. Quadratic equations of the forms ax2 = c and ax2 + bx = c appear. Several values of π occur in Baudhayana's Sulbasutra since when giving different constructions Baudhayana uses different approximations for constructing circular shapes. Constructions are given which are equivalent to taking π equal to 676/225 (where 676/225 = 3.004), 900/289 (where 900/289 = 3.114) and to 1156/361 (where 1156/361 = 3.202). None of these is particularly accurate but, in the context of constructing altars they would not lead to noticeable errors.






