Aryabhatta – the Indian Mathematician-Astronomer

Aryabhata
Statue of Aryabhata on the grounds of IUCAA, Pune.

Aryabhata or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Aryabhatiya (499 CE, when he was 23 years old) and the Aryabhatta-siddhanta.

Aryabhata mentions in the Aryabhatiya that he was born in 476. Aryabhata called himself a native of Kusumapura or Pataliputra (present day Patna). Some people were saying that he was born in the South of India mostly Kerala. But it cannot be disproved that he was not born in Patliputra and then traveled to Magadha where he was educated and established a coaching center. His first name is Arya which is a South Indian name and “Bhatt or “Bhatta” a normal north Indian name which could be seen among the trader people in India.

Aryabhata mentions “Lanka” on several occasions in the Aryabhatiya, but his “Lanka” is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini. It is interesting that Aryabhatta himself have mentioned himself at only 3 places and as Aryabhata in his work Aryabhatiya.

However, it is quite certain that they had gone to Kusumapura higher education at some point of time and were also there for some time. Aryabhatta has identified Kusumapura as Patliputra (modern Patna). In the last days of the Gupta empire, they used to live there, it was the time which is known as the golden age of India.

Education

It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhaskara I (CE 629), identify Kusumapura as Pataliputra, modern Patna. A verse mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, 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.

Aryabhatiya

Aryabhata’s work are known only from the Aryabhatiya. His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). Among them Aryabhatiya is the only text that has survived to this day. It is also occasionally referred to as Arya-shatas-aShTa (means, Aryabhata’s 108). It is a small treatise written is 108 verses. The text consists of the 108 verses and 13 introductory verses, and is divided into four padas or chapters Gitikapada (13 verses), Ganitapada (33 verses), Kalakriyapada (25 verses), Golapada (50 verses).

Aryabhatiya was translated into Latin in the 13th century. Through this translation, European mathematician got to know methods for calculating the areas of triangles, volumes of spheres as well as square and cube root.

The Zero and Place value system

Aryabhata greatest contribution has to be ZERO, for which he became immortal. Aryabhata did not use the Brahmi numerals. He used Sanskritic tradition from Vedic times. He used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form. Aryabhata did not use a symbol for zero, a French mathematician has argued in favour that knowledge of zero was implicit in Aryabhata’s place-value system as a place holder for the powers of ten with null coefficients. This was later proved when Bhatta used null coefficients as place holder for powers of tens in his place value system.

Approximate value of π

Aryabhata was first Indian who calculated value of pie. He wrote in Sanskritic :

caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

Which means “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” and that value is 3.1416 which is accurate to five significant figures. It is speculated that Aryabhata used the word asanna (approaching), to mean that not only is this an approximation but that the value is irrational. If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert.

Aryabhatta was aware that the earth rotates on its axis. The earth rotates round the sun and the moon moves round the earth. He discovered the 9 planets position and related them to their rotation round the sun. Aryabhatta said the light received from planets and the moon is gotten from sun. He also made mention on the eclipse of the sun, moon, day and night, earth contours and the 365 days of the year as the exact length of the year. Aryabhatta also revealed that the earth circumference is 24835 miles when compared to the modern day calculation which is 24900 miles.

Another aspect of mathematics that he worked upon is arithemetic, algebra, quadratic equations, trigonometry and sine table.

Trigonometry

In Ganitapada 6, Aryabhata gives the area of a triangle as

tribhujasya phalashariram samadalakoti bhujardhasamvargah

Which means:  “for a triangle, the result of a perpendicular with the half-side is the area.”

Modern names “sine” and “cosine” are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin.

Astronomy

Aryabhatta was the first to explain how the Lunar Eclipse and the Solar Eclipse happened. His system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or “equator”. 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.

Aryabhatta calculated the sidereal rotation 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).

Aryabhatta was the first one to make an attempt at measuring the earth’s circumference. Aryabhata accurately calculated the earth’s circumference as 24835 miles( 39968.0582 km ), which was only 0.2 % smaller than the actual value of 24,902 miles ( 40075.884 km ) . This approximation remained the most accurate for over a thousand years.

 

Honour

  • 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.

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