Question

achievment of brahmagupta

Answer 1

Brahmagupta was a highly accomplished ancient Indian astronomer and mathematician who was the first to give rules to compute with zero. He is best remembered as the author of the theoretical treatise ‘Brāhmasphuṭasiddhānta’ ("Correctly established doctrine of Brahma"). He composed his texts in elliptic verse in Sanskrit, as was common practice in Indian mathematics of his time. The ‘Brāhmasphuṭasiddhānta’ was a seminal work in astronomy which went on have a deep influence not just in the development of astronomy in India, but also had a great impact on Islamic mathematics and astronomy. An orthodox Hindu, he took care not to antagonize his own religious leaders but was very bitter in criticizing the ideas advanced by rival astronomers hailing from the Jain religion. He was among the few thinkers of his era who had realized that the earth was not flat as many believed, but a sphere. He was much ahead of his contemporaries and his mathematical and astronomical calculations remained among the most accurate available for several centuries. He is believed to have written many works though only a few survive today. In addition to being an accomplished astronomer, he was also a much revered mathematician. His ‘Brāhmasphuṭasiddhānta’ is the first book that mentions zero as a number and also gives rules for using zero with negative and positive numbers.

Answer 2

was the director of the astronomical observatory of Ujjain, the center of Ancient Indian mathematical astronomy.

• wrote four books about astronomy and mathematics, the most famous of which is Brahma-sphuta-siddhanta ( Brahma’s Correct System of Astronomy, or The Opening of the Universe.)

• said solving mathematical problems was something he did for pleasure.

• was the first person in history to define the properties of the number zero. Identifying zero as a number whose properties needed to be defined was vital for the future of mathematics and science.

• defined zero as the number you get when you subtract a number from itself.

• said that zero divided by any other number is zero.

• said dividing zero by zero produces zero. (Although, this seems reasonable, Brahmagupta actually got this one wrong. Mathematicians have now shown that zero divided by zero is undefined – it has no meaning. There really is no answer to zero divided by zero.)

• was the first person to discover the formula for solving quadratic equations.

• wrote that pi, the ratio of a circle’s circumference to its diameter, could usually be taken to be 3, but if accuracy were needed, then the square-root of 10 (this equals 3.162…) should be used. This is about 0.66 percent higher than the true value of pi.

• indicated that Earth is nearer the moon than the sun

• incorrectly said that Earth did not spin and that Earth does not orbit the sun. This, however, may have been for reasons of self-preservation. Opposing the Brahmins’ religious myths of the time would have been dangerous.

• produced a formula to find the area of any four-sided shape whose corners touch the inside of a circle. This actually simplifies to Heron’s formula for triangles.

• said the length of a year is 365 days 6 hours 12 minutes 9 seconds.

• calculated that Earth is a sphere of circumference around 36,000 km (22,500 miles).

Brahmagupta established rules for working with positive and negative numbers, such as:

• adding two negative numbers together always results in a negative number.

• subtracting a negative number from a positive number is the same as adding the two numbers.

• multiplying two negative numbers together is the same as multiplying two positive numbers.

• dividing a positive number by a negative, or a negative number by a positive results in a negative number.