The Great Indian mathematician "Aryabhata"
Aryabhatta, also known as Aryabhatta I or Aryabhata (476-550?), was a famous Indian mathematician and astronomer, born in a place called Taregana, in Bihar (though some people do not agree with the evidence). Taregana (also spelled as Taragna) which literally means songs of stars in Bihari, is a small place situated nearly 30 km from Patna, which was then known as Kusumpura later Pataliputra, the capital of the Gupta Empire. This is the very empire that has been dubbed as the “golden period in Indian history”. The best introduction to the genius of past is seen in the words of Bhaskara I who said, “Aryabhatta is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world”.
Aryabhatta, the Indian mathematician
head of Nalanda University at Kusumpura
(modern Patna)
What was his name?
Varahamihira, the younger contemporary of Aryabhatta also mentions him as “Aryabhata”. In addition to this, Bhaskara I too mentions him as Aryabhata. It seems as if the correct name was Aryabhata and not Aryabhatta. This could mean that “Bhatta” was not his surname but as part of his first name. In fact, there is a lot of confusion about his name too. Perhaps he was called Arya and his surname was Bhat or Bhatta!
Where did Aryabhatta come from?
There is some disagreement about this birth place. Some are of the view that he was born in Patliputra while some are of the view that he was born in Kerala and moved to Patliputra and lived there. Those who say that he was in Bihar is because of this name. His name “Arya” and “Bhatta” indicates that he was from North India. His suffix “Bhatta” could have been either part of his name or his surname, till date it’s not known if this is correct or not. It is interesting to note that Aryabhatta himself have mentioned himself at only 3 places and as “Aryabhata” in his work Aryabhatiya. The reason for not considering Kerala as his birthplace is that nowhere in his works he has mentioned Kerala. In addition, all works of Aryabhatta is in Sanskrit and Sanskrit was not used in Kerala. So to claim that Aryabhatiya was written in Kerala has no credibility. Furthermore, he has been identified by numerous mathematicians and in Arabic translations as someone who hailed from Kusumpura (modern Patna), the capital of Magadha. It therefore appears that Aryabhatta was born, lived, flourished and worked in Magadha. He has also been described as the head of the Nalanda University.
Aryabhatta mentions himself as Aryabhata
Influence of Aryabhatta on science and mathematics
Aryabhatta is considered to be one of the mathematicians who changed the course of mathematics and astronomy to a great extent. He is known to have considerable influence on Arabic science world too, where he is referred to as Arjehir. His notable contributions to the world of science and mathematics includes the theory that the earth rotates on its axis, explanations of the solar and lunar eclipses, solving of quadratic equations, place value system with zero, and approximation of pie (π).
Aryabhatta approximatted pi
Aryabhatta exerted influence on the Indian astronomical tradition to such an extent that his presence was felt in neighboring countries and cultures also. There have been various translations of his work among which the Arabic translation during the 820CE is very significant. When mathematical students are confused with trigonometry even today, Aryabhatta had defined sine, cosine, versine and inverse sine back in his era, influencing the birth of trigonometry. The signs were originally known as jya, kojya, utkrama-jya and otkram jya. In Arabic they were translated as jiba and kojiba, which later when being translated into Latin was misunderstood to be ‘fold in a garment’ by Gerard of Cremona, who stated it as sinus, which meant fold in Latin. Aryabhatta was the first mathematician to detail both sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to 4 decimal places. Aryabhatta’s astronomical calculations influenced the Arabians, who used the trigonometric tables to compute many astronomical tables. His calendared calculation has been in continuous use in India, on which the present day Panchangam is based. His studies are also base for the national calendars of Iran and Afghanistan today.
Aryabhatiya
It is known that Aryabhatta has authored at least three astronomical books, in addition he also wrote some free stanzas. Among them “Aryabhatiya” is the only text that has survived to this day, whereas unfortunately his other works have been extinct. It is a small treatise written is 118 verses, which summarizes the Hindu mathematics of that time. This great mathematical masterpiece of the past starts with 10 verse introduction, which is then followed by mathematical section which is written in 33 verses that gives out 66 mathematical rules, but there is no proof to go with it. The mathematical part of the Aryabhatiya is about algebra, arithmetic, plane trigonometry and spherical trigonometry in addition to advanced mathematics on continued fractions, quadratic equations, sums of power series and a table of sines.
Quadratic equation by Aryabhatta
The next section consists of 25 verses which gives us glimpse into the planetary models. The final section of the book is dedicated to sphere and eclipses which runs into 50 verses. He states that the moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony where eclipses were believed to be caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by earth or those shadows that fall on earth. It is amazing how Aryabhatta could explain both lunar and solar eclipse so accurately.
Statue of Aryabhatta at Inter-University Centre for
Astronomy and Astrophysics at Pune (India)
There is some argument over the claim of Aryabhatta being the inventor of place value system that made use of zero. Georges Ifrah, in his work ‘Universal history of numbers: From prehistory to the invention of the computer (London, 1998)’ writes in work, “..it is extremely likely that Aryabhatta knew the sign for zero and the numerals of the place value system”. Georges Ifrah has studied the works of Aryabhatta and found that the counting and mathematical work carried out by him would have been not possible without zero or place value system.
Honouring Aryabhatta
The Indian ISRO (Indian Space Research Organization) named its first satellite after the genius mathematician and astronomer. A research establishment has been set up in Nainital, called the Aryabhatta Research Institute of Observational Sciences (ARIOS) to honor his contribution to the field of science. There is also a lunar crater and a species of bacteria discovered by ISRO named after Aryabhatta.
Some of the works of Aryabhatta include
- Aryabhatta worked out the value of pi.
- He worked out the area of a triangle. His exact words were, “ribhujasya phalashariram samadalakoti bhujardhasamvargah” which translates “for a triangle, the result of a perpendicular with the half side is the area”.
- He discussed the idea of sin.
- He worked on the summation of series of squares and cubes (square-root and cube-root).
- He talks about the “rule of three” which is to find the value of x when three numbers a, b and c is given.
- Aryabhatta calculates the volume of a sphere.
- Aryabhatta described the model of the solar system, where the sun and moon are each carried by epicycles that in turn revolve around the Earth. He also talks about the number of rotations of the earth, describes that the earth rotating on its axis, the order of the planets in terms of distance from earth.
- Aryabhatta describes the solar and lunar eclipses scientifically.
- Aryabhatta describes that the moon and planets shine by light reflected from the sun.
- Aryabhatta calculated the sidereal rotation which is the rotation of the earth with respect to the stars as 23 hours, 56 minutes and 4.1 seconds.
- He calculated the length of the sidereal year as 365 days, 6 hours, 12 minutes and 30 seconds. The actual value shows that his calculations was an error of 3 minutes and 20 seconds over a year.
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