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