Aryabhata

Aryabhata (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta. Aryabhata provides no information about his place of birth. The only information comes from Bhaskara I, who describes Aryabhata as āśmakīya, "one belonging to the aśmaka country .It is speculated that Aryabhata might have been the head of the Nalanda University as well. Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.

Some archeological evidences suggest that Aryabhata could have originated from the present day Kodungallur in Kerala region. For instance, one hypothesis was that aśmaka (Sanskrit for "stone") may be the region in Kerala that is now known as Kodungallur

Aryabhatiya

His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.

The Aryabhatiy

There are 108 verses in the text. It is written in the very terse style typical of sutra literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four chapters such as Gitikapada: (13 verses), Ganitapada (33 verses), Kalakriyapada (25 verses) and Golapada (50 verses). This work presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries.

Mathematics

He contributed a lot in the area of mathematics such as Place value system and zero. While he did not use a symbol for zero, However he did not use the Brahmi numerals.And he worked on the approximation for pi (π), and may have come to the conclusion that π is irrational. He also contributed in Trigonometry, algebra and Indeterminate equations .His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry.

Astronomy

He shows his interest In astronomy also. He may have believed that the planet's orbits as elliptical rather than circular.

Motions of the solar system

Aryabhata correctly insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view in other parts of the world, that the sky rotated. This is indicated in the first chapter of the Aryabhatiya, where he gives the number of rotations of the earth in a yuga, and made more explicit in his gola chapter. He described a geocentric model of the solar system, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. In this model, which is also found in the Paitāmahasiddhānta (c. CE 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast). The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."

The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.  Another element in Aryabhata's model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata.  Aryabhata states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse.

Sidereal periods

Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days)is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).

Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age was particularly influential. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis.

Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, India's first satellite Aryabhata and the lunar crater Aryabhata are named in his honour. An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, India. The inter-school Aryabhata Maths Competition is also named after him, as is Bacillus Aryabhata, a species of bacteria discovered by ISRO scientists in 2009.