# Frases de Aryabhata

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## Aryabhata

Data de falecimento: 550

Ariabata ou Ariabata I foi o primeiro dentre os grandes matemáticos-astrônomos da Idade Clássica dos matemáticos e astrônomos indianos. Seu trabalho inclui o Ariabatiia e o Aria-Sidanta.

### „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.“

—  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.

### „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.“

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

### „He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. 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 series is the sum of the cubes.“

—  Aryabhata
Roger Cooke in: The history of mathematics: a brief course http://books.google.co.in/books?id=z-ruAAAAMAAJ, Wiley, 7 October 1997, p. 207.

### „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.“

—  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.

### „His fame rests mainly on his Aryabhatiya, but from the writings of Varahamihira (Sixth century AD), Bhaskara I, and Brahmagupta (seventh century) it is clear that earlier he composed the Aryabhata Siddhantha (voluminous) is not extant. It is also called Ardharatrika Siddhanta, because in it the civil days were reckoned from one midnight to the next; 34 verses on astronomical instruments from this have been quoted by Ramakrishna Aradya.“

—  Aryabhata
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, In, p. 244.

### „Aryabhatiya, an improved work, is product of mature intellect, which he wrote when he was 23 years old. Unlike in the Aryabhata siddhanta, the civil days are reckoned from one sunrise to the next, a practice which is still prevalent among the followers of Hindu calendar.“

—  Aryabhata
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, In, p. 244.

### „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.“

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

### „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.“

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

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

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

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

—  Aryabhata
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, 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.

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### „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.“

—  Aryabhata
In: 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 The irrationality of pi was proved by Lambert in Europe in the year 1761.