MTH/110

December 10, 2012

Biography - Aryabhata, the Indian mathematician

Aryabhata (476 CE – 550 CE) was the first Hindu mathematician and astronomers from India. He wrote couple of treatise about mathematics and astronomy. Some of them were lost. His most famous works Aryabhatiya completed in 499 CE and the Arya-Siddhanta. Aryabhatiya consists of 108 verses, in which Aryabhata wrote about the mathematics and astronomy at the age of 23 in 499 CE. He was born in India at Asmaka or Kusumapura in 476 CE. There is no clear evidence of the place of birth (Indian Streams Research General, September 2012). Aryabhata studied in Kusumapura and stayed there for some time. The evidences from Hindu, Buddhist tradition, and Bhaskara I (629 CE) recognize Kusumapura as Pataliputra, currently known as Patna. Aryabhata was the head of an institution at Kusumapura. The University of Nalanda was in Pataliputra at the time. This university had an astronomical observatory that forces the belief that Aryabhata was the head of the Nalanda University. Aryabhata set up an observatory at the Sun temple in Taregana, Bihar (Aryabhata – Indian Mathematician). Aryabhatiya deals with mathematics and astronomy. That consists of an introduction containing astronomical tables and Aryabhata’s system of phonemic number notation. This work consists of three sections: Ganita (means mathematics), Kala-kriya (means Time calculations), and Gola (means Sphere). Ganita covers decimal number system, algorithms for square and cubic roots, geometric measurements, the algorithm for Pi, tables of sines using Pythagorean Theorem, quadratic equations, proportions, and the solution of linear equations. This discusses the Aryabhata’s method to solve the mathematical problem, Kuttaka (means pulverizer) also known as Aryabhata’s algorithm. This algorithm suggests breaking a problem in smaller fractions. Kala-kriya speaks about astronomy. It is about treating planetary motion and include the definition of various units for time, eccentric, epicyclic planetary motion modes, longitude, and latitude. Gola discusses the plane trigonometry to spherical geometry. It also has prediction of solar and lunar eclipses and explicit statement about westward motion of stars because of the spherical rotation of the Earth about its axis (Indian Streams Research General, September 2012). The Arya-siddhanta was the work on astronomical computations. Surya Siddhanta was the base of this work and considered the start of the day at the midnight, as opposed to sunrise according to 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 types, bow-shaped and cylindrical. Bakhshali Manuscript discussed the place-value system first in the 3rd century. Georges Ifrah, the mathematician from France, acknowledged that awareness of zero by Aryabhata in place-value system because of a place holder for the powers of 10 with null coefficients. Instead of using Brahmi numerals Aryabhata continued the tradition from Vedic times by using letters of the alphabet for denoting numbers, expressing quantities, such as the table of sines in a mnemonic form (Indian Streams Research General, September 2012). The Surya Siddhanta laid foundational rules to determine the true motions of the luminaries and introduced the sine, cosine trigonometric functions. Aryabhata devised the formulae for calculating the area of triangle and circle. He also devised the same for pyramid and sphere. Formulae for triangle and circle were correct. Most historians claimed that formulae for sphere and pyramid were incorrect. He created a table of sines and...

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