Aryabhata

On that day, India became only the world’s 11th nation to send a satellite into orbit. More importantly, the Aryabhata satellite helped lay the foundation on which India built its impressive space program. Today, India is among the few nations that has sent a probe to the moon, and only one of four to achieve interplanetary orbit. In 1971, Indira Gandhi, the then-Prime Minister, received a message from Moscow via the Indian ambassador. The message informed her that the Soviet Academy of Sciences was ready to assist India in launching its first satellite – no doubt, the Kremlin was concerned by a possible collaboration between India and the US. In the end, India decided to take them up on their offer, and Aryabhata would be launched with the Soviet Union’s help. However, just as a launch date was looking like a possibility, Vikram Sarabhai, ISRO's founder died. His death brought the whole Indian space program to a standstill – the satellite project looked to be in serious trouble. Determined to press ahead despite this setback, Dr. Rao and his team were able to finish work on the satellite and a launch date was decided. At this point, the satellite was still without a name. To secure her support, the team of scientists turned to the Prime Minister, Indira Gandhi, to bestow it with a moniker. She chose “Aryabhata”, after the great 5th Century CE mathematician and astronomer. Among his many other discoveries, Aryabhata was famous for creating a system of phonemic number notat...

Aryabhatiya ( Āryabhaṭīya) or Aryabhatiyam ( Āryabhaṭīyaṃ), a Structure and style [ ] Aryabhatiya is written in • Gitikapada (13 verses): large units of time— • Ganitapada (33 verses): covering • Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the • Golapada (50 verses): Geometric/trigonometric aspects of the It is highly likely that the study of the Aryabhatiya was meant to be accompanied by the teachings of a well-versed tutor. While some of the verses have a logical flow, some do not, and its unintuitive structure can make it difficult for a casual reader to follow. Indian mathematical works often use word numerals before Aryabhata, but the Aryabhatiya is the oldest extant Indian work with Cf. Contents [ ] The Aryabhatiya contains 4 sections, or Adhyāyās. The first section is called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an introduction called the "Dasageethika" or "Ten Stanzas." This begins by paying tribute to not Brāhman), the "Cosmic spirit" in Hinduism. Next, Aryabhata lays out the numeration system used in the work. It includes a listing of Most of the mathematics is contained in the next section, the "Ganitapada" or "Mathematics." Following the Ganitapada, the next section is the "Kalakriya" or "The Reckoning of Time." In it, Aryabhata divides up days, months, and years according to the movement of celestial bodies. He divides up history astronomi...

Aryabhata Astronomer Specialty Astronomy, mathematics Born 476 CE prob. Ashmaka Died 550 CE Nationality Indian Aryabhata was one of the great mathematicians and astronomers from the classical era in India. In fact, he is considered to be the first great mathematician in a long line of visionary mathematicians who would emerge from India from the classical era onward. His published works were many years ahead of their time and a significant amount of modern mathematics and astronomy can be traced back to the studies and works associated with him. Early Life and Education Aryabhata was born around 475 A.D. in the region known as Ashmaka. Historians cannot be completely sure when he was born, but one of his works notes it was written around 3,600 years into the Kali Yuga, so a rough estimation about the time in which he was born can be ascertained. It is really not even known were for sure he was born as Ashmaka. It might be considered a nickname of sorts for Maharashtra or Dhaka. The remaining historical records from the era piece together a hypothesis about his advanced level education taking place at Kusumapura and that he lived in this area for quite some time. There is some speculation that Kusumapura is actually another region and may really be Pataliputra, which was actually the location of where a major astronomical observatory was located. Therefore, it would make great sense that this was where he would have invested a great deal of time learning to be a great astro...

Indian mathematician and astronomer Āryabhaṭa (c. 920 – c. 1000) Maha-Siddhanta. The numeral II is given to him to distinguish him from the earlier and more influential Maha-Siddhanta have been discovered from Maha Siddhanta [ ] Aryabhata wrote Maha-Siddhanta, also known as Arya-siddhanta, The initial twelve chapters deal with topics related to mathematical astronomy and cover the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars. The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc. Other contributions to maths [ ] Aryabhata II also deduced a method to calculate the cube root of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they pla...

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The northern Indian mathematician and astronomer, Aryabhata, born in 476, wrote one of the earliest known Indian mathematics and astronomy books, the Aryabhatiya, in 499 (Katz, p. 212). In Section II, Stanza 22, of the Aryabhatiya, he wrote: The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the (original) series is the sum of the cubes. (Katz, 217) The first sentence gives the formula from pages 1 and 3, above, for the sum of the squares; the second says, in our notation, that $$(1 + 2 + 3 + \cdots + n)^2 = 1^3 + 2^3 + 3^3 + \cdots + n^3.$$ If we replace \(1 + 2 + 3 + · · · ­+ n\) by \(=3n(n+1)\) cubes can be seen by noting that the shell can be built using an n x ( n + 1) slab for the floor and two adjoining wall slabs with dimensions n x n and n x ( n + 2). This will result in an outside shell with height n, length n + 1, and width n + 2. The inside shells should be constructed with dimensions like those of the outside shell. (See Joseph, George Gheverghese, 2000, The Crest of the Peacock, Princeton University Press, pp. 295-296, and the references given for Exercise 4.) Exercise 6: How might early mathematicians have discovered the identity from Exercise 1? Provide at least four examples and write the identity in terms of n, where n is a positive integer. For solutions to these exercises, click Janet Beery (Universit...

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Born: 476, probably in Ashmaka Died: 550 (at age 74), location unknown Nationality: Indian Famous For: Early mathematician who calculated the value of pi Aryabhata (476-550) was an Indian Aryabhata’s Early Life Aryabhata came from southern India, but his precise place of birth is not known. Some authorities suggest that Kerala is the most likely location, while others believe that Dhaka or Maharashtra are more probable. It is, however, generally accepted that he studied at an advanced level in Kusumapura in modern-day Patna, where he remained for some years. A contemporary poem places Aryabhata as the manager of a scientific institution; the precise nature of the body is not given, but there are grounds for suspecting that it may have been linked to the astronomical observatory that was maintained there by the University of Nalanda. The Aryabhatiya While studying at the university, Aryabhata produced the Aryabhatiya, his major work. Written at the age of just 23, it ranges widely across mathematics and astronomy, but is particularly notable for its calculations regarding planetary periods. The value given for the length of the Earth’s astronomical day differs from the true value by only a matter of minutes. Aryabhata also worked out a value for pi that equates to 3.1416, very close to the approximations still used today. Using this value, he was able to calculate that the Earth had a circumference of 24,835 miles. This is correct to within 0.2%, and remained the best figur...

Born: 476, probably in Ashmaka Died: 550 (at age 74), location unknown Nationality: Indian Famous For: Early mathematician who calculated the value of pi Aryabhata (476-550) was an Indian Aryabhata’s Early Life Aryabhata came from southern India, but his precise place of birth is not known. Some authorities suggest that Kerala is the most likely location, while others believe that Dhaka or Maharashtra are more probable. It is, however, generally accepted that he studied at an advanced level in Kusumapura in modern-day Patna, where he remained for some years. A contemporary poem places Aryabhata as the manager of a scientific institution; the precise nature of the body is not given, but there are grounds for suspecting that it may have been linked to the astronomical observatory that was maintained there by the University of Nalanda. The Aryabhatiya While studying at the university, Aryabhata produced the Aryabhatiya, his major work. Written at the age of just 23, it ranges widely across mathematics and astronomy, but is particularly notable for its calculations regarding planetary periods. The value given for the length of the Earth’s astronomical day differs from the true value by only a matter of minutes. Aryabhata also worked out a value for pi that equates to 3.1416, very close to the approximations still used today. Using this value, he was able to calculate that the Earth had a circumference of 24,835 miles. This is correct to within 0.2%, and remained the best figur...

Indian mathematician and astronomer Āryabhaṭa (c. 920 – c. 1000) Maha-Siddhanta. The numeral II is given to him to distinguish him from the earlier and more influential Maha-Siddhanta have been discovered from Maha Siddhanta [ ] Aryabhata wrote Maha-Siddhanta, also known as Arya-siddhanta, The initial twelve chapters deal with topics related to mathematical astronomy and cover the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars. The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc. Other contributions to maths [ ] Aryabhata II also deduced a method to calculate the cube root of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they pla...