Baudhayana 

Born: about 800 BC in India Died: about
800 BC in India To write a biography of Baudhayana is
essentially impossible since nothing is known of him except that he
was the author of one of the earliest Sulbasutras. We do not know his
dates accurately enough to even guess at a life span for him, which
is why we have given the same approximate birth year as death year.
He was neither a mathematician in the sense that we would
understand it today, nor a scribe who simply copied manuscripts like
Ahmes. He would certainly have been a man of very considerable
learning but probably not interested in mathematics for its own sake,
merely interested in using it for religious purposes. Undoubtedly he
wrote the Sulbasutra to provide rules for religious rites and it
would appear an almost certainty that Baudhayana himself would be a
Vedic priest. The mathematics given in the
Sulbasutras is there to enable the accurate construction of altars
needed for sacrifices. It is clear from the writing that Baudhayana,
as well as being a priest, must have been a skilled craftsman. He
must have been himself skilled in the practical use of the
mathematics he described as a craftsman who himself constructed
sacrificial altars of the highest quality. The
Sulbasutras are discussed in detail in the article Indian
Sulbasutras. Below we give one or two details of Baudhayana's
Sulbasutra, which contained three chapters, which is the oldest which
we possess and, it would be fair to say, one of the two most
important. 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 p 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 p
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. An
interesting, and quite accurate, approximate value for v2 is given in
Chapter 1 verse 61 of Baudhayana's Sulbasutra. The Sanskrit text
gives in words what we would write in symbols as
v2 = 1 + 1/3 + 1/(34)  1/(3434)= 577/408 which
is, to nine places, 1.414215686. This gives v2 correct to five
decimal places. This is surprising since, as we mentioned above,
great mathematical accuracy did not seem necessary for the building
work described. If the approximation was given as
v2 = 1 + 1/3 + 1/(34) then the error is of the
order of 0.002 which is still more accurate than any of the values of
p. Why then did Baudhayana feel that he had to go for a better
approximation? Article by: J J O'Connor
and E F Robertson
Source:www.history.mcs.standrews.ac.uk/Mathematicians



