Aryabhata

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Aryabhata

  1. 1. GREAT MATHEMATICIAN
  2. 2. Aryabhata (476–550 CE) was the first in the line of great mathematician-astronomersfrom the classical age of Indian mathematics and Indian astronomy. His most famousworks are the Āryabhaṭ īya (499 CE, when he was 23 years old) and the Arya-siddhanta.Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the KaliYuga, when he was 23 years old. This corresponds to 499 CE, and implies that he wasborn in 476Aryabhata was born in Taregna (literally, song of the stars), which is a small town inBihar, India, about 30 km (19 mi) from Patna (then known as Pataliputra), the capital cityof Bihar State.It is fairly certain that, at some point, he went to Kusumapura for advanced studiesand that he lived there for some time. Both Hindu and Buddhist tradition, as well asBhāskara I (CE 629), identify Kusumapura as Pāṭ aliputra, modern Patna. A versementions that Aryabhata was the head of an institution (kulapati) at Kusumapura, and,because the university of Nalanda was in Pataliputra at the time and had an astronomicalobservatory, it is speculated that Aryabhata might have been the head of the Nalandauniversity as well.[1]Aryabhata is also reputed to have set up an observatory at the Suntemple in Taregana, Bihar.
  3. 3. arth is y that E n. on to sa d the su rst pers s arounHe wa s the fi revolve a l and itspheric
  4. 4. Great Works >>• Aryabhatas work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (c. 820 CE), was particularly influenced. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhatas followers believed that the Earth rotated on its axis.• His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.• Aryabhatas astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th c.) and remained the most accurate ephemeris used in Europe for centuries.• Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam,[33] versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. calender.
  5. 5. • He gave the formula (a + b)2 = a2 + b2 + 2ab.• He taught the method of solving the following problems:
  6. 6. • Indeterminate equations• A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to equations that have the form ax + by = c, a topic that has come to be known as diophantine equations. This is an example from Bhāskaras commentary on Aryabhatiya: – Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7• That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts might date to 800 BCE. Aryabhatas method of solving such problems is called the kuṭṭ aka (कु ट क ) method. Kuttaka means "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. Today this algorithm, elaborated by Bhaskara in 621 CE, is the standard method for solving first-order diophantine equations and is often referred to as the Aryabhata algorithm. The diophantine equations are of interest in cryptology, and the RSA Conference, 2006, focused on the kuttaka method and earlier work in the Sulbasutras.
  7. 7. Indias firs t s atellite and the lunar crater A ryabhataare named in his honour. A n Ins titute for conductingres earch in as tronomy, as trophys ics and atmos pherics ciences is the A ryabhatta Res earch Ins titute ofObs ervational S ciences (A RIOS ) near Nainital, India. Theinter-s c hool A ryabhata Maths C ompetition is als o namedafter him,as is Bacillus aryabhata, a s pecies of bacteriadis covered by IS RO s cientis ts in 2009.
  8. 8. Nivedita Tomar XII-A 12017MATHEMATICS

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