Aryabhata
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- This article is about the Indian astronomer Aryabhata, For information on Arybhata the first Indian satellite, see Aryabhata (satellite).
Aryabhata (आर्यभट) Āryabhaṭa) (476 – 550) is the first of the great mathematician-astronomers of the classical age of India. He lived in Kusumapura, which his commentator Bhāskara I (629 AD) identifies with Pataliputra (modern Patna).
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Aryabhatiya
Template:Main Aryabhata's Magnum Opus, the Āryabhatīya, is a concise text of 123 stanzas in Sanskrit that provide insight into his discoveries. It presents astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun (in other words, it was heliocentric). He believes that the Moon and planets shine by reflected sunlight and he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon. His value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is only 3 minutes 20 seconds longer than the true value of 365 days 6 hours 9 minutes 10 seconds. This book is divided into four chapters: (i) the astronomical constants and the sine table (ii) mathematics required for computations (iii) division of time and rules for computing the longitudes of planets using eccentrics and epicycles (iv) the armillary sphere, rules relating to problems of trigonometry and the computation of eclipses. In this book, the day was reckoned from one sunrise to the next, whereas in his "Āryabhata-siddhānta" he took the day from one midnight to another. There was also difference in some astronomical parameters.
Aryabhata also gave close approximation for Pi. In the Aryabhatiya, he wrote: "Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given." In other words, π ≈ 62832/20000 = 3.1416, correct to four rounded-off decimal places.
He also propounded the Heliocentric theory of the universe, thus predating Copernicus by almost one thousand years. The 8th century Arabic translation of the Āryabhatīya was translated into Latin in the 13th century, before the time of Copernicus. Through this translation, European mathematicians may have learned methods for calculating square and cube roots, and it is also possible that Aryabhata's work had an influence on European astronomy.
Aryabhata was the first astronomer to make an attempt at measuring the Earth's circumference since Erastosthenes (circa 200 BC). Aryabhata accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles. This approximation remained the most accurate for over a thousand years.
Mathematics
One of the books of Aryabhatiya is on mathematics. Aryabhata describes the kuttaka algorithm to solve indeterminate equations. In recent times, this algorithm has also been named the Aryabhata algorithm.
He also created a novel alphabetic code to represent numbers that is now called the Aryabhata cipher.
Aryabhata, in his work Aryabhata-Siddhanta, first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versine, and inverse sine. His works also contained the earliest tables of sine values and versine (1 − cosine) values, in 3.75° intervals from 0° to 90°, to an accuracy of 3 decimal places. He used the words jya for sine, kojya for cosine, ukramajya for versine, and otkram jya for inverse sine. The words jya and kojya eventually became sine and cosine respectively after a mistranslation (see Etymology above).
Continued relevance
Aryabhata's methods of astronomical calculations have been in continuous use for practical purposes of fixing the Panchanga (Hindu calendar).
Recently his name has been in the news because RSA Conference 2006 chose their theme to be ancient Vedic Mathematics and Aryabhata. Indocrypt 2005 had an invited talk on vedic mathmatics. As more and more conferences with information security professionals focus on vedic Mathematics, it is believed that vedic Mathematics will have profound effect on cryptographic systems.
Confusion of identity
There has been some confusion regarding Aryabhatta's identity. Another notable Indian mathematician named Aryabhata flourished sometime between 950 and 1100 C.E and is often referred to as Aryabhata II. The Persian historian al-Biruni incorrectly believed that there were two famous Indian mathematicians named Aryabhata who lived around 500 C.E. The subsequent confusion from this blunder ensued until it was disproved in 1926 when B Datta showed that al-Biruni's two Aryabhattas were one and the same person.
Overview
- Accurately computed pi
- Explained and computed solar eclipses and lunar eclipses
- Expounded a heliocentric model of the solar system
- Accurately computed the length of earth's revolution around the sun.
External links
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