|
|
|
|
Medieval Mathematicians in India
Associated to Place:
AncientWorlds >
The Orient >
India >
articles
-- by
Early Indian scholars made invaluable contributions to later western knowledge of mathematics and astronomy.
Early Indian mathematicians and astronomers made invaluable contributions to later western knowledge of these subjects. From the sixth century, these men were exploring and creating systems of calculation which were only discovered much later in Europe. While they recorded their findings, most were written in Sanskrit verse. Not only was there a lack of communication with the rest of the world, but a distrust on the part of western scientists of all things from what they considered the decadent and backward east. There were many accomplished mathematicians in medieval India, of which the following five are considered to be the most prominent. Aryabhata I (476-550) Aryabhata lived most of his life in Kusumapura, which is thought to be close to Pataliputra, in Bihar. In his book, Aryabhatiya, he set forth his theories on arithmetic, algebra, and plane and spherical trigonometry. His three other astronomical texts have been lost. Aryabhata reasoned that the earth spun on its axis and was aware of the relativity of motion. He thought that the earth rotated around the sun and correctly explained the causes of solar and lunar eclipses, which in his time were thought to be caused by the demon Rahu. He calculated that the length of a year was 365 days, 6 hours, 12 minutes, and 30 seconds, which was only slightly less than 12 1/2 minutes off from what we know to be true today. He attempted to mathematically measure the Earth's circumference, the first astronomer to do so since Erastosthenes in 200 BCE. Aryabhata's calculation of 24,835 miles was but a little less than the actual figure, 24,902 miles. Today, the Panchanga Hindu calendar is still based on his methods of astronomical calculation. Compare Aryabhata's calculations with today's figures Brahmagupta (598-670) Brahmagupta was born in 598 in Rajasthan, in northwest India. He wrote his masterpiece, Brahmasphuta Siddhanta, which means The Opening of the Universe, in 628. This treatise was translated into Arabic in the eighth century in Baghdad and became well-known in the east as Sindhind, greatly influencing Islamic astronomy. Brahmagupta became the head of the astronomical center at Ujjain, in central India, the foremost mathematical center in India of the time. One of Brahmagupta's major contributions was the concept of zero and negative numbers. He also invented algorithms for square roots and the solution of quadratic equations, and a formula for determining the values of sines. He devised methods to calculate solar and lunar eclipses and the motion and positions of the planets. He thought that the earth was round, but did not believe that the earth moved. Brahmaugupta produced the Khand Khadyak, a major addendum to his original treatise, in 665, when he was 67 years old. Bhaskaracharya (1114-1185) The son of a famed astrologer, Bhaskaracharya was born in Karnataka. Sometimes referred to as Bhaskara II, his name means Bhaskara the Teacher. Like Brahmagupta, Bhaskaracharya headed the observatory at Ujjain. The subjects of his six works include arithmetic, algebra, trigonometry, calculus, geometry, astronomy. There is a seventh book attributed to him which is thought to be a forgery. Bhaskaracharya discovered the concept of differentials, and contributed a greater understanding of number systems and advanced methods of equation solving. He was able to accurately calculate the sidreal year, or the time it takes for the earth to orbit the sun. There is but a scant difference in his figure of 365.2588 days and the modern figure of 365.2596 days. There is an interesting legend about his daughter Lilavati, for whom Bhaskaracharya named his book on arithmetic. According to a Persian translation, when Lilavati became of marriageable age, Bhaskaracharya cast her horoscope to determine the most propitious day and hour for her wedding to take place. The signs told him that if she was not married at a particular place at a particular time, the bridegroom would die shortly after the wedding. To prevent this, Bhaskaracharya made a small hole in the bottom of a cup which he then put into a jug of water. He had calculated that the cup would sink to the bottom at the appropriate hour for the wedding. Though he warned his daughter not to disturb this arrangement, Lilavati's curiosity led her to lean over the device, and in doing so, a pearl fell off her dress and blocked the hole in the cup. The cup never sank and poor Lilavati was never able to be married. Her father wrote her a mathematics manual, which was supposed to console her and to keep her occupied as she studied its contents. Some scholars have disputed this tale as mere fantasy, citing no evidence of Bhaskaracharya ever having a daughter, and some even think that Lilavati may have been his wife. Madhava (1340-1425) Founder of the Kerala School, Madhava is considered by many to have been the greatest of the mathematician astronomers in medieval India. He is credited with laying the foundations for the development of calculus and modern mathematical analysis, and made contributions in the fields of mathematical analysis, infinite series development, trigonometry, geometry and algebra. Though all of his mathematical works are lost, we know from later references that Madhava discovered trigonometric functions that were not developed in Europe for another two hundred years. He was also able to correctly expand the values of pi to eleven places. Some of his astronomy texts survive, in which he explained the methods he used to calculate the positions of the moon every 36 minutes and for predicting the motions of the planets. Nilakantha Somayaji (1455-1545) Nilakantha Somayaji was from a Brahmin family in Kerala, in southern India. His name, Somayaji, came from his worship of Soma, the Hindu god of the moon. He expanded and improved Madhava's theories on infinite series in his astronomy text, Tantrasamgraha, which was written in 1501. The interesting thing about this treatise is that it offers mathematical proofs of his theories, which was unusual in Indian works of the time. Nilakantha developed an accurate heliocentric model of the solar system and wrote several other treatises on the planets, spherical geometry, algebra, and calculus. sources: History of Indian Science Aryabhata The Elder Wikipedia - Aryabhata Brahmagupta Brahmagupta Bhaskara Wikipedia - Bhaskara Madhava of Sangamagramma Wikipedia - Madhava of Sangamagrama Nilakantha Somayaji |
Study
~ Table of Contents ~
|
