Âryabhata citations (11 citations)

Âryabhata: 11 citations 0 J'aime

Âryabhata: Citations en anglais

“He is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.”

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Aryabhata

Bhaskara I, quoted in: J J O'Connor and E F Robertson "Aryabhata the Elder".

“The development of Indian trigonometry, based on sine as against chord of the Greeks, a necessity for astronomical calculations with his own concise notation which expresses the full sine table in just one couplet for easy remembrance. One of the two methods suggested by him for the sine table is based on the property that the second order sine differences were proportional to sines themselves.”

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Aryabhata

In, P.245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

“In geometry his greatest achievement was an accurate value of π.”

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Aryabhata

His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.
In, p. 245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

“In Indian astronomy, the prime meridian is the great circle of the Earth passing through the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on the Earth's equator.”

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Aryabhata

In Aryabhatiya quoted in: J J O'Connor and E F Robertson Aryabhata the Elder http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html, School of Mathematics and Statistics University of St Andrews, Scotland.

“Use of better planetary parameters, the innovations in astronomical methods, and the concise style of exposition of Aryabhatiya makes it an excellent text book on Astronomy. As opposed to the geostationary theory, Aryahabata held the view that the earth rotates on its axis. His estimate of the period of the sidereal rotation of earth was 23 hours 56 min, and 4.1 s is close to the actual value.”

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Aryabhata

In, p. 254.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

“His work, called Aryabhatiya, is composed of three parts, in only the first of which use is made of a special notation of numbers. It is an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, …., 100 etc. The other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed in Southern India, the numbers 1-19 being designated by consonants, etc.”

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Aryabhata

Florian Cajori in: A History of Mathematical Notations http://books.google.co.in/books?id=_byqAAAAQBAJ&pg=PT961&dq=Notations&hl=en&sa=X&ei=Wz65U5WYDIKulAW1qIGYDA&ved=0CBwQ6AEwAA#v=onepage&q=Notation&f=false, Courier Dover Publications, 26 September 2013, p. 47.

“Translates to: for a triangle, the result of a perpendicular with the half-side is the area.”

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Aryabhata

Source: Arijit Roy “The Enigma of Creation and Destruction”, p. 27 from the Ganitapada, quoted in "The Enigma of Creation and Destruction".

“Translates to: Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached. Thus according to the rule ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.”

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Aryabhata

The irrationality of pi was proved by Lambert in Europe in the year 1761.
Source: Arijit Roy The Enigma of Creation and Destruction http://books.google.co.in/books?id=JFmUQqYzA7wC&pg=PA27, Author House, 28 October 2011, p. 27