This document gives a chronology of computing at Columbia University, as best I can piece it together, written mainly in JanFeb 2001, updated periodically since then. Aryabhata Wikipediaryabhaa. Born. 47. 6 CEKusumapura Pataliputra present day Patna1Died. CEResidence. India. Academic background. Influences. Surya Siddhanta. Download Fundamental Ephemeris Computations Pdf' title='Download Fundamental Ephemeris Computations Pdf' />Academic work. Era. Gupta era. Main interests. Download Fundamental Ephemeris Computations Pdf' title='Download Fundamental Ephemeris Computations Pdf' />Mathematics, astronomy. Notable worksryabhaya, Arya siddhanta. Notable ideas. Explanation of lunar eclipse and solar eclipse, rotation of Earth on its axis, reflection of light by moon, sinusoidal functions, solution of single variable quadratic equation, value of correct to 4 decimal places, circumference of Earth to 9. Influenced. Lalla, Bhaskara I, Brahmagupta, Varahamihira. Overview. Panchngams are published in India by many learned authors, societies, academies, and universities. Different publications differ only minutely, at least. PyPIIntended Audience. Aryabhata IAST ryabhaa or Aryabhata I 476550 CE was the first of the major mathematicianastronomers from the classical age of Indian mathematics and. Content_public/Journal/mnras/446/2/10.1093_mnras_stu2152/2/m_stu2152fig6.jpeg?Expires=1489514387&Signature=OnsOCLcbvhYhyQOYs91SFMenh~OWH8zw5hoFRQf95MK1YR5YAhJiWXVqbgBvfqb~I6tGjUjOBpHqKit2v0fkZl0EI8jcH9uRJjgdDq-scWonkUvqCTx7TwjhX1LMMNMgjokt~MPpVwC0kKJGBhzn1cYT04k~ZTiTTkSot-qM6TWDNIKuAgJ3MfZyCkNvVlvmC3mh~bRlekVw-tkHf8J4D3PjpFkg3b-w0cJblhvCn7zSBsxRq5wL10xQW7Gb0oMc-rUdP5Av~2ZA7OjmiA6scGmgB2fJrzgQckuoYR6LteYFMJ7wiPzY6PPXjNf37oAHYjlDSdXiPlF69biad92grw__&Key-Pair-Id=APKAIUCZBIA4LVPAVW3Q' alt='Download Fundamental Ephemeris Computations Pdf' title='Download Fundamental Ephemeris Computations Pdf' />Aryabhata IAST ryabhaa or Aryabhata I23 4. CE45 was the first of the major mathematician astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the ryabhaya 4. CE, when he was 2. Download Skill And Personality Development Program Centre For Sc/St Students. Arya siddhanta. 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 Brahmaguptas references to him in more than a hundred places by name. Furthermore, in most instances Aryabhatta would not fit the metre either. Time and place of birth. Aryabhata mentions in the Aryabhatiya that it was composed 3,6. Kali Yuga, when he was 2. This corresponds to 4. CE, and implies that he was born in 4. Aryabhata called himself a native of Kusumapura or Pataliputra present day Patna, Bihar. Other hypothesis. Bhskara I describes Aryabhata as makya, one belonging to the Amaka country. During the Buddhas time, a branch of the Amaka people settled in the region between the Narmada and Godavari rivers in central India. It has been claimed that the amaka Sanskrit for stone where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala. This is based on the belief that Kouallr was earlier known as Koum Kal l r city of hard stones however, old records show that the city was actually Koum kol r 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 Aryabhatas main place of life and activity however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala. K. Chandra Hari has argued for the Kerala hypothesis on the basis of astronomical evidence. 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. Education. It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhskara I CE 6. Kusumapura as Paliputra, modern Patna. A verse 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 of the Nalanda university as well. Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar. 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 Aryabhatas contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. 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 chh. Ay. A 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 types, bow shaped and cylindrical. A third text, which may have survived in the 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, Ab Rayhn al Brn. Aryabhatiya. Direct details of Aryabhatas work are known only from the Aryabhatiya. The name Aryabhatiya is due to later commentators. Aryabhata himself may not have given it a name. His disciple Bhaskara I calls it Ashmakatantra or the treatise from the Ashmaka. It is also occasionally referred to as Arya shatas a. Sh. Ta literally, Aryabhatas 1. 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 1. Gitikapada 1. 3 verses large units of timekalpa, manvantra, and yugawhich present a cosmology different from earlier texts such as Lagadhas Vedanga Jyotisha c. BCE. There is also a table of sines jya, given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4. Ganitapada 3. 3 verses covering mensuration ketra vyvahra, arithmetic and geometric progressions, gnomon shadows shanku chh. Ay. A, simple, quadratic, simultaneous, and indeterminate equations kuaka. Kalakriyapada 2. Asa, k. Shaya tithis, and a seven day week with names for the days of week. Golapada 5. 0 verses Geometrictrigonometric 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, c. CE and by Nilakantha Somayaji in his Aryabhatiya Bhasya, 1. 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. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhatas place value system as a place holder for the powers of ten with nullcoefficients. However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form. Approximation of Aryabhata worked on the approximation for pi, and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam gaitapda 1. History of surveying instruments by Land Surveyor. History of surveying instruments Published on Mar 1. History of surveying instruments Primer by Land Surveyors United Community http landsurveyorsunited.