how did Aryabhatta contribution help traders in trade?
Answers
Aryabhatta was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.
He is the author of several treatises on mathematics and astronomy, some of which are lost. His main works are Aryabhatiya and Arya-siddhanta.
Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries. The work was written in verse couplets and deals with mathematics and astronomy.
Arya-siddhanta circulated mainly in the northwest of India and, through Iran, had a profound influence on the development of Islamic astronomy.It is one of the earliest astronomical works to assign the start of each day to midnight.
His contribution to mathematics:
Place value system and zero:
The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients.
Value of pi :
He also worked on the approximation for pi , and may have come to the conclusion that pi is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.
Trigonometry :
He gave the area of a triangle as:
tribhujasya phalashariram samadalakoti bhujardhasamvargah
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
He also discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord".
Algebra :
In Aryabhatiya, he provided elegant results for the summation of series of squares and cubes:
and
Explanation:
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