Ganitapada (33 verses covering mensuration ( kṣetra vyāvahāra arithmetic and geometric progressions, gnomon / shadows ( shanku - chhaya simple, quadratic, simultaneous, and indeterminate equations ( kuṭaka ). Kalakriyapada (25 verses different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month ( adhikamAsa kshaya-tithi s, and a seven-day week with names for the days of week. Golapada (50 verses geometric/ trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of day and night, rising of zodiacal signs on horizon, etc. In addition, some versions cite a few colophons added at the end, extolling the virtues of the work, etc. The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara i ( Bhashya,. 600 CE) and by nilakantha somayaji in his Aryabhatiya bhasya, (1465 CE). Mathematics Place value system and zero The place-value system, first seen in the 3rd-century bakhshali manuscript, was clearly in place in his work.
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8 A third text, which may have survived in the beautiful Arabic translation, is Al ntf or Al-nanf. It claims that it is a translation by Aryabhata, but the sanskrit name of this work is not known. Probably dating from the 9th century, it is mentioned by the persian scholar and chronicler of India, abū rayhān al-Bīrūnī. 8 Aryabhatiya main article: Aryabhatiya direct details of Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. It is also occasionally referred to as Arya-shatas-aShTa (literally, aryabhata's 108 because there are 108 verses in the text. It is written in the very terse style typical of sutra literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four summary pāda s or chapters: Gitikapada : (13 verses large units of time— kalpa, manvantra, and yuga —which present a cosmology different from earlier texts such as Lagadha's Vedanga jyotisha. There is also a table of sines ( jya given in a single verse.
7 a verse revelation mentions that Aryabhata was the head of an institution ( kulapa ) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head. 7 Aryabhata is also reputed to have set up an observatory at the sun temple in Taregana, bihar. 13 Works Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines. The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara. This work appears to be based on the older Surya siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments: the gnomon ( shanku-yantra a shadow instrument ( chhaya-yantra possibly angle-measuring devices, semicircular and circular ( dhanur-yantra / chakra-yantra a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, and water clocks of at least two.
7 8 It has been claimed that presentation the aśmaka (Sanskrit for "stone where Aryabhata originated may be the present day kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala. 9 This is based on the belief that Koṭuallūr was earlier known as friend Koṭum-Kal-l-ūr city of hard stones however, old records show that the city was actually koṭum-kol-ūr city of strict governance. Similarly, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used to suggest that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside kerala, and the Aryasiddhanta was completely unknown in Kerala. Chandra hari has argued for the kerala hypothesis on the basis of astronomical evidence. 10 Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini. 11 Education It is fairly certain that, at some point, he went to kusumapura for advanced studies and lived there for some time. 12 Both Hindu and Buddhist tradition, as well as Bhāskara i (CE 629 identify kusumapura as Pāṭaliputra, modern Patna.
Contents, biography, name, while there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the " bhatta " suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus, 7 including, brahmagupta 's references to him. 1, furthermore, in most instances "Aryabhatta" would not fit the meter either. 7, time and place of birth. Aryabhata mentions in the, aryabhatiya that it was composed 3,600 years into the. Kali yuga, when he was 23 years old. This corresponds to 499 ce, and implies that he was born in 476. 5 Aryabhata called himself a native of Kusumapura or Pataliputra (present day patna, bihar ). 1 Other hypothesis Bhāskara i describes Aryabhata as āśmakīya, "one belonging to the aśmaka country." During the buddha's time, a branch of the aśmaka people settled in the region between the narmada and Godavari rivers in central India.
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Top, personal Life legacy, aryabhatas work was of great influence in the Indian nurse astronomical tradition and influenced several neighboring cultures through translations. Some of his works are cited by Al-Khwarizmi, and in the 10th century by Al-Biruni. Continue reading Below, the Aryabhata Knowledge University (aku patna, has been established by the government of Bihar in his honor for the development and management of educational infrastructure related to technical, medical, management and allied professional education. Indias first satellite Aryabhata is named in his honor. At the Aryabhata research Institute of Observational Sciences (arios) near nainital, India, research in astronomy, astrophysics and atmospheric sciences is conducted.
Top, trivia, named after the great Indian astronomer of the same name, indias first satellites image used to appear on the reverse of Indian 2 rupee banknotes. Named after the great Indian astronomer is the remnant of a lunar impact crater located in the eastern sea of Tranquility on the moon. Submerged by lava-flow, now only an arc-shaped ridge remains. For other uses, see, aryabhata (disambiguation). Aryabhata iast : Āryabhaṭa ) or, aryabhata i 2 3 (476550. Ce ) 4 5 was the first of the major mathematician - astronomers from the classical age of, indian mathematics and, indian astronomy. His works include the Āryabhaṭīya (499 ce, when he was 23 years old) 6 and the.
He discussed sine by the name of ardha-jya or half-chord. Like other ancient Indian mathematicians, he too was interested in finding integer solutions to diophantine equations with the form ax by c; he called it the kuṭaka (meaning breaking into pieces) method. His contribution to the study of Algebra is immense. In Aryabhatiya, aryabhata provided elegant results for the summation of series of squares and cubes through well tried formulae. Continue reading Below, his system of astronomy was called the audayaka system, in which days are reckoned from uday, dawn at lanka or equator. His later writings, which apparently proposed the ardha-rAtrika, or midnight model, are lost.
He correctly believed that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, challenging the prevailing view. In Aryabhatiya, he writes that setting and rising of planets is a perception similar to that of someone in a boat going forward sees an unmoving (object) going backward. He correctly asserted that the planets shine due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth, and not caused by a demon called Rahu! He correctly deduced that the orbits of the planets are ellipses; this is another great discovery not credited to him but to johannes Kepler (a german astronomer, born ad 1571). Top, major Works, aryabhatas major work, aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature, and has survived to modern times. The Aryabhatiya covers arithmetic, algebra, and trigonometry.
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Ganitapada, the second chapter of Aryabhatiya has 33 verses covering mensuration (kṣetra vyāvahāra arithmetic and geometric progressions, gnomon or shadows (shanku-chhaya simple, quadratic, simultaneous, and indeterminate equations. Aryabhatiyas third chapter Kalakriyapada explains different units of time, a method for determining the positions of planets for a given day, yardage and a seven-day week with names for the days of week. The last chapter of the Aryabhatiya, summary golapada describes geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, shape of the earth, cause of day and night, and zodiacal signs on horizon. Continue reading Below, he did not use a symbol for zero; its knowledge was implicit in his place-value system as a place holder for the powers of ten with null coefficients. He did not use the Brahmi numerals, and continued the sanskritic tradition from Vedic times of using letters of the alphabet to denote numbers, expressing quantities in a mnemonic form. He worked on the approximation for pi thus — add four to 100, multiply by eight, and then add 62,000, the circumference of a circle with a diameter of 20,000 can be approached. It is speculated that Aryabhata used the word āsanna (approaching to mean that not only is this an approximation, but that the value is incommensurable or irrational. In Ganitapada, he gives the area of a triangle as: for a triangle, the result of a perpendicular with the half-side is the area.
its head too. Direct details of his work are known only from the Aryabhatiya. His disciple Bhaskara i calls it Ashmakatantra (or the treatise from the Ashmaka). The Aryabhatiya is also occasionally referred to as Arya-shatas-aShTa (literally, aryabhatas 108 because there are 108 verses in the text. It also has 13 introductory verses, and is divided into four pādas or chapters. Aryabhatiyas first chapter, gitikapada, with its large units of time — kalpa, manvantra, and Yuga — introduces a different cosmology. The duration of the planetary revolutions during a mahayuga is given.32 million years.
He london was the first known astronomer to devise a continuous counting of solar days, designating each day with a number. He asserted that the planets shine due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth. His observations discount the flat earth concept, and lay the foundation for the belief that earth and other planets orbit the sun. Continue reading Below, aryabhata. Childhood early life, aryabhatas birthplace is uncertain, but it may have been in the area known in ancient texts as Ashmaka, which may have been Maharashtra or Dhaka or in Kusumapura in present day patna. Some archaeological evidence suggests that he came from the present day kodungallur, the historical capital city of Thiruvanchikkulam of ancient Kerala - this theory is strengthened by the several commentaries on him having come from Kerala. He went to kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist traditions, as well as Bhāskara i, the 7th Century mathematician, identify kusumapura as modern Patna.
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Continue reading Below, aryabhata was an acclaimed mathematician-astronomer. He was born in Kusumapura (present day patna) in Bihar, India. His contribution to mathematics, science and astronomy is immense, and yet he has not been accorded the recognition in the world history of paper science. At the age of 24, he wrote his famed Aryabhatiya. He was aware of the concept of zero, as well as the use of large numbers up to 1018. He was the first to calculate the value for pi accurately to the fourth decimal point. He devised the formula for calculating areas of triangles and circles. He calculated the circumference of the earth as 62,832 miles, which is an excellent approximation, and suggested that the apparent rotation of the heavens was due to the axial rotation of the earth on its axis.