# Aryabhata

Aryabhata I ( Devanagari: आर्यभट, Aryabhata, * 476 in Ashmaka; † 550 ) was a major Indian mathematician and astronomer. Born in Ashmaka, he later lived in Kusumapura, which later Bhaskara I ( 629) as Pataliputra, the modern Patna identified.

## Mathematics

It is believed that the concept of the number " 0 " (zero) back to Aryabhata, although only at the zero Brahmagupta obviously treated as a separate count, and for computing rules are shown.

Aryabhata determined the circle of pi for that time very precisely to 3.1416 and seems to have already guessed that this is an irrational number. He could draw square roots and cube roots, and solve different linear and quadratic equations; he further developed the trigonometry. Even his sines are written in ancient Indian tradition in verse. As his greatest mathematical performance but is the " indeterminate analysis " for generalized Diophantine equations to look at. Mediated by Muslim mathematicians got his mathematical knowledge, indirectly, in the later medieval Europe.

## Astronomy

Aryabhatas main work " Aryabhatiya ", which is written in verse form, was found in the 19th century in southern India in several manuscripts. On these manuscripts based the modern editions and translations. The verse related a very concise presentation. Detailed comments authored the first Bhaskara I. to 600 AD

In this work he first developed his own system of numbers, the Aryabhata code. Furthermore, (Mercury, Venus, Mars, Jupiter and Saturn) are for sun, moon and the planets then known values are given, allow an accurate calculation of their positions and ephemerides under a geocentric system. But Aryabhata also already taught that the earth revolves on its axis once a day, and some numerical values and formulations suggest a heliocentric system located behind it; perhaps he had already realized that the planetary orbits are ellipses. He determined the circumference of the earth by only 0.2 % too small compared with the modern value. Aryabhata already had a very clear idea of the relativity of motion.

Aryabhata wrote that 1,582,237,500 rotations of the Earth correspond 57,753,336 Mondumläufen. This is an extremely accurate calculation of these fundamental astronomical " constant" ( 1.582.237.500/57.753.336 = 27.3964693572 ) and perhaps the oldest calculated with such precision astronomical relationship at all. So he determined the sidereal day (one rotation of the earth relative to the star background ) to 23 hours 56 minutes and 4.1 seconds, compared with the modern value of 23:56:4,091 hours. Due to the slowing of the Earth's rotation by tidal friction, this ratio is time dependent. Aryabhatas value was exactly for the time around 1600 BC

Aryabhatas ephemeris are very accurate for its era, but diverge for periods before and after quickly from today's bills. This is due to the fact that it establishes a chronological hypothesis. He was like many astronomers in Greece, Mesopotamia, India and China believe that the periods of the seven classical planets ( Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn) are commensurable, ie, that there be a common multiple of the periods needs. (See above for example the calculation of the sidereal day. ) But then from time to time all the planets have gathered together at the same point of the ecliptic. Aryabhata had calculated that such a Great Conjunction of 17-18. February 3102 BC took place in 1 ° in the constellation Aries. This he began with the outbreak of the Kali Yuga era equal. The starting point for the ephemeris is February 19th 499 AD (60 * 60 years after the beginning of the age ), and they are on the meridian of Ujjain ( 75.767 ° east longitude relative to Greenwich), the prime meridian all Hindu astronomers relative. Since the planets were actually true near the Aries point, but distributed over nearly a constellation, its ephemeris apply only to the time of his observations. Roger Billiards has calculated from the ephemeris, when and where Aryabhata did his observations. As time he determined to 513 AD and as meridian 57 ° East. The deviation from the meridian of Ujjain according to 1.3 hours is due to the slowing of the Earth's rotation by tidal friction, which was determined independently from Chinese observations of eclipses to about 1.6 hours for the time around 500 AD. The great importance that Aryabhata attributed the Great Conjunctions was supported by the Islamic astronomers Albumasar ( 787-866 ) resumed. He influenced rabbinical astrologers like Isaac Abrabanel and Kepler's conjecture that the star of Bethlehem was a Dreifachkonjunktion of Jupiter and Saturn.

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

## Honors

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

## Namesake

According to Al -Biruni you went long assumed that there were two scientists named Aryabhata in the 5th century, but acted it is one and the same person. Some scholars held the rediscovered only in the 19th century manuscripts in addition to modern forgeries. Billards statistical analyzes show that the observations were made by 510 AD. And in particular, you could not then calculate the slowing of the Earth's rotation. This is in line with the biographical entry in the " Aryabhatiya " that he was 23 years old 3600 years and 9 months after the beginning of the Kali Yuga, he was so born in the year 476 AD.

Besides Aryabhata I. but is also an Indian astronomer Aryabhata II known from which a " Mahasiddhanta " is preserved. The survival data Aryabhatas II are uncertain and 950-1100 AD are given.

## Works

- Walter Eugene Clark ( ed.): The Aryabhatiya of Aryabhata. An Ancient Indian Work on Mathematics and Astronomy. The University of Chicago Press 1930 ( Reprinted 2006 ).
- Aryabhatiya of Aryabhata, critical edition by KS Shukla and KV Sarma (1976 )