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Did You Know?
By D.P. Agrawal

Question: Did you know who was Aryabhatt and what was his date?

Answer: Aryabhatt was a great mathematician and astronomer of ancient India.

Date of Aryabhata:
Kâlakriya 20: When sixty times sixty years and three quarters of the yugas (of this yuga) had elapsed, twenty three years had then passed since my birth

(In Aryabhata's system of measuring time, 3600 of the Kali era corresponds to mean noon at Ujjain, on March 21, 499 CE (Sunday). So Aryabhata was born in 476 CE.) All other authors known by name are later to Aryabhata I, and mention his theories while refuting them or correcting them. The dates for Varahamihira have been verified also by independent techniques.)

Question: Did you know that Aryabhatt had propounded the view that earth was round.

Answer: He compared the Earth to a Kadamba flower as explained in the following quaotes.

Gola 6: The globe of the Earth stands (supportless) in space at the centre of the celestial sphere....The Earth is circular on all sides.

Gola 7: Just as the bulb of a Kadamba flower is surrounded by blossoms on all sides, so also is the globe of the Earth surrounded by all creatures whether living on land or in water.

(The very term Gola means sphere or round. Vatesvara, explicitly mentions a popular belief about the Earth being supported on the back of a turtle, and points out its deficiencies, "What does the turtle rest upon, etc". But no other reputed astronomer seems to have taken such possibilities seriously enough even to contest them.)

Question: Did you know that Aryabhatt propounded in the 5th Century AD that the Earth rotates and not the celestial sphere?

Gola 9: Just as a man in a moving boat sees the stationary objects on the land moving in the opposite direction, so also the stationary stars are seen by a person at Lanka as moving exactly towards the West. (Lanka is an imaginary point on the equator at which the Meridian of Ujjayini intersects the Equator. Ujjayini is the modern-day Ujjain. Thus, Aryabhata's Lanka is below the current-day Lanka. The Meridian of Ujjayini is was later copied by instituting the Meridian of Greenwich. )

Gola 10: It only appears to an observer at Lanka as if the celestial sphere and the asterisms and planets move to the West...to cause their rising and setting.

(This view is rejected by later authors, like Varahamihira, Brahmagupta etc. on the grounds that if it is the Earth that rotates, then clothes on a line will fly, and the falcon, which rises high in the sky will not be able to find its way back. Others say, the tops of trees will be destroyed, the ocean will invade the land etc.)

Question: Did you know that Aryabhatt had worked out the duration of the day at the poles?

Gola 16: The gods living in the north at the Meru mountain (north pole) see one half of the Bhagola (celestial sphere with its centre at the centre of the earth) as revolving from left to right (i.e., clockwise); the demons living in the south at Badvâmukha (south pole) see the other half rotating from right to left (i.e., anti-clockwise).

Gola 17: The gods (at the north pole) see the sun after sunrise for half a solar year; so do the demons (at the south pole). Those living on the moon see the sun for half a lunar month; the humans here see it for half a civil day.

(Wooden and iron models were used to demonstrate the spheres. Bhagola is the celestial sphere centred at the centre of the earth, while Khagola is the sphere centred on the observer. The principal circles of the Bhagola are the celestial equator, the ecliptic etc., while the principal circles of the Khagola are the horizon, the meridian, the prime vertical etc. For the related concepts of spherical astronomy, consult any text on spherical astronomy.)

Question: Did you know that Aryabhatt had given an accurate value of pi (p)?

Rational approximation to pi

Ganita 10: 104 multiplied by 8 and added to 62000 is the approximate circumference of a circle whose diameter is 20,000.

(That is, pi = 62832/20000 = 3.1416. This value of pi was widely used in the Arabic world. In Europe, this value is cited by Simon Stevin in his book on navigation, The Haven Finding Art, as the value known to the "ancients" which he states (correctly) as far superior to any value known to the Greeks. Unlike what current-day historians would have us believe, Egypt does not mean Greece to Simon Stevin. In any case Aryabhata's value is better than that of Ptolemy (3.141666), who lived in Alexandria, in Egypt. Simon Stevin, a Dutch mathematician, astronomer and navigator, introduced the decimal system in Europe, c. 1580, and gives a table of sine values like Aryabhata, correcting the earlier table given by Nunes. Better values of pi were subsequently obtained in Europe using the "Gregory" series for the arctangent, and faster convergent methods, all of which are found in works of the Aryabhata school, which were imported into Europe in the 16th and 17th c. (Gregory does not claim originality.) The Sanskrit term for approximate is asanna, a term also used in the sulba sutra. The Chinese had a better value of pi than Aryabhata, just as al Kashi had a more accurate value of pi than Nîlkantha. However, none of those values had the potential of the calculus, and neither Chinese nor al Kashi had equally accurate sine values. (Ptolemy does not even mention sines.) The Chinese value may well have been a fluke, while al-Kashi's value was based on extremely laborious computation. Neither had the future potential or the sweep that Aryabhata's approximation techniques had. These techniques were later developed by his school into the "Taylor" series for arctangent, the sine and the cosine.)

(Information on Aryabhatt and his work was kindly given by C.K. Raju, Professor of Math and Computer Science, Bhopal, India. His email ID is: c_k_raju@vsnl.net)

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