Science: Old is Gold-Great Indian Scientist Brahmagupta

Brahmagupta a very very old mathematician,astronomer etc.He had proposed the Gravitational pull of Earth some hundreds years before Sir Isaac Newton proposed it.Brahmagupta was the first to use zero as a number. He gave rules to compute with zero. Contrary to popular opinion, negative numbers did not appear first in Brahmasputa siddhanta.Brahmagupta's most famous work is his Brahmasphutasiddhanta. It is composed in elliptic verse, as was common practice in Indian Mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta's mathematics was derived. In BrahmasputhaSiddhanta, Multiplication was named Gomutrika. In the beginning of chapter twelve of his Brahmasphutasiddhanta, entitled Calculation, Brahmagupta details operations on fractions. The reader is expected to know the basic arithmetic operations as far as taking the square root, although he explains how to find the cube and cube-root of an integer and later gives rules facilitating the computation of squares and square roots. He then gives rules for dealing with five types of combinations of fractions, $\tfrac{a}{c} + \tfrac{b}{c}$ , $\tfrac{a}{c} \cdot \tfrac{b}{d}$ , $\tfrac{a}{1} + \tfrac{b}{d}$ , $\tfrac{a}{c} + \tfrac{b}{d} \cdot \tfrac{a}{c} = \tfrac{a(d+b)}{cd}$ , and $\tfrac{a}{c} - \tfrac{b}{d} \cdot \tfrac{a}{c} = \tfrac{a(d-b)}{cd}$ .Brahmagupta went on to give a recurrence relation for generating solutions to certain instances of Diophantine equations of the second degree such as

N x 2 + 1 = y 2

(called Pell's Equation) by using the Euclidean Algorithm. The Euclidean algorithm was known to him as the "pulverizer" since it breaks numbers down into ever smaller pieces.
In 665 Brahmagupta devised and used a special case of the Newton–Stirling interpolation formula of the second-order to interpolate new values of the sine function from other values already tabulated. The formula gives an estimate for the value of a function

f

at a value a + xh of its argument (with h > 0 and −1 ≤ x ≤ 1) when its value is already known at a − h, a and a + h.
The formula for the estimate is:

$f( a + x h ) \approx f(a) + x \left(\frac{\Delta f(a) + \Delta f(a-h)}{2}\right) + \frac{x^2 \Delta^2 f(a-h)}{2!}.$

where Δ is the first-order forward-difference operator, i.e.

$\Delta f(a) \ \stackrel{\mathrm{def}}{=}\ f(a+h) - f(a).$ Great Brahmagupta great.This is only what we can say

Science

Sunday 29 May, 2011

Old is Gold-Great Indian Scientist Brahmagupta

No comments:

Post a Comment