# Aryabhata

Aryabhata I. ( Devanagari : आर्यभट, Āryabhaṭa; * 476 in Ashmaka , † around 550) was an important Indian mathematician and astronomer . Born in Ashmaka, he later lived in Kusumapura , which Bhaskara I (629) later identified as Pataliputra , today's Patna .

## mathematics

It is assumed that the concept of the number “0” ( zero ) goes back to Aryabhata, although it is not until Brahmagupta that zero is obviously treated as an independent number and calculation rules are given for it.

Aryabhata determined the circle number Pi very precisely to 3.1416 for that time and seems to have already suspected that it was an irrational number . He could take square roots and cube roots , and solve various linear and quadratic equations ; he also developed trigonometry . Even his sine tables are written in verse in the ancient Indian tradition. His greatest mathematical achievement, however, is the "indefinite analysis" for generalized Diophantine equations . Mediated by Muslim mathematicians, his mathematical knowledge also indirectly reached later medieval Europe.

## astronomy

Modern statue of Aryabhata at the Inter-University Center for Astronomy and Astrophysics in Pune

Aryabhata's main work "Aryabhatiya" , which is written in verse, was found in several manuscripts in southern India in the 19th century. Modern editions and translations are based on these manuscripts . The verse form required a very concentrated presentation. Bhaskara I was the first to write detailed comments around AD 600.

In this work he first developed his own number system, the Aryabhata code . Furthermore, values ​​are given for the sun , moon and the planets known at that time ( Mercury , Venus , Mars , Jupiter and Saturn ), which enable an exact calculation of their positions or ephemeris within the framework of a geocentric system. Aryabhata also taught that the earth rotates once a day around its own axis, and some numerical values ​​and formulations suggest that there is a heliocentric system behind it ; possibly he had already recognized that the planetary orbits are ellipses . He determined the circumference of the earth by only 0.2% too small compared to the modern value. Aryabhata already had very clear ideas about the relativity of movement.

Aryabhata writes that 1,582,237,500 rotations of the earth correspond to 57,753,336 lunar orbits. This is an extremely accurate calculation of this fundamental astronomical “constant” (1,582,237,500/57,753,336 = 27.396 469 , today's value 27.321 662 ) and perhaps the oldest astronomical ratio ever calculated with such accuracy. He determined the sidereal day (one revolution of the earth in relation to the star background) to be 23 hours 56 minutes and 4.1 seconds, up to rounding equal to the modern value of 23: 56: 4.091 hours. Due to the slowing down of the earth's rotation due to tidal friction, this ratio is time-dependent. Aryabhata's value was exactly for the time around 1600 BC. Chr.

Aryabhata's ephemeris are very accurate for his epoch, but diverge quickly from today's calculations for times before and after. This is due to the fact that he introduces a chronological hypothesis. Like many astronomers in Greece, Mesopotamia, India and China he was convinced that the periods of the 7 classical planets (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn) are commensurable , i.e. that is, there must be a common multiple of the periods. (See, for example, the calculation of the sidereal day above.) But then from time to time all planets must meet at the same point on the ecliptic . Aryabhata had calculated that such a major conjunction would take place on 17./18. February 3102 BC Took place in 1 ° in the constellation Aries . He equated this with the beginning of the Kali Yuga age. The starting point for the ephemeris is February 19, 499 AD (60 * 60 years after the beginning of the age), and they are on the meridian of Ujjain (75.767 ° east longitude from Greenwich ), the prime meridian of all Hindu astronomers , based.
Since the planets were actually close to the Aries point , but distributed over almost a constellation, his ephemeris are only valid for the time of his observations. Roger Billard calculated from the ephemeris when and where Aryabhata made his observations. He determined the point in time to be around AD 513 and the meridian 57 ° East. The deviation from the meridian of Ujjain corresponding to 1.3 hours is explained by the slowing down of the earth's rotation due to tidal friction, which was independently determined from Chinese observations of eclipses to be around 1.6 hours for the time around 500 AD.
The great importance Aryabhata attached to the great conjunctions was taken up again by the Islamic astronomer Albumasar (787-866). He influenced rabbinical astrologers like Isaak Abrabanel and Kepler's hypothesis that the star of Bethlehem was a triple conjunction of Jupiter and Saturn.

His astronomical calculation methods are still used to create the Pancanga Hindu calendar.

## Honors

The International Astronomical Union (IAU) honored him by naming the lunar crater Aryabhata . India's first artificial satellite , which was launched on April 19, 1975, was called "Aryabhata" .

## Namesake

According to Al-Biruni , it was long assumed that there were two scientists with the name Aryabhata in the 5th century , but they were one and the same person. In addition, some scholars considered the manuscripts, which were only found again in the 19th century, to be modern forgeries. However, billiards statistical analysis shows that the observations were made around AD 510. In particular, it was not yet possible to calculate the slowdown in the earth's rotation at that time . This coincides with the biographical information in the "Aryabhatiya" that he was 23 years old 3600 years and 9 months after the beginning of Kali-Yuga, that is, he was born in AD 476.

In addition to Aryabhata I, an Indian astronomer Aryabhata II is also known, from whom a "Mahasiddhanta" has been handed down. The dates of Aryabhatas II's life are uncertain and are given between 950 and 1100 AD.

## Works

• Walter Eugene Clark: The Aryabhatiya of Aryabhata. An Ancient Indian Work on Mathematics and Astronomy. The University of Chicago Press 1930 ( online at archive.org , reprinted 2006), translation and annotation of the Aryabhatiya .
• Aryabhatiya of Aryabhata , critical edition by KS Shukla and KV Sarma (1976)

## literature

• Kurt Elfering: The Mathematics of Aryabhata I , Munich 1975, ISBN 3-7705-1326-6
• Bartel Leendert van der Waerden: The Astronomy of the Greeks , Darmstadt 1988 (with many comments on Aryabhata)
• Roger Billard: L'astronomie Indienne , Paris 1971
• Roger Billard: Aryabhata and Indian Astronomy , Indian Journal of History of Sciences 12 (1977) 207
• Franz Krojer: Astronomy of late antiquity, the zero and aryabhata , difference publishing house, Munich 2009