## ARYABHATA 1

*"I delved deep in the astronomical theories, true and false and rescued the precious sunken jewel of the knowledge by means of the best of my intellect and by the grace of God" *

### (Aryabhata, AD 476-550)

Although there is confusion among historians whether Aryabhata I and Aryabhata II (another mathematician, who apparently lived 400 years later) were two persons or really one and the same, there is no confusion about the former being the acclaimed mathematician/astronomer. He was born in 476 AD in Kusumapura (present day Patna) in Bihar, North India- although some have conjectured that he was actually born in Kerala, Tamil Nadu or Andhra Pradesh in South India or Bengal in East India.

Aryabhata is a rare gem in Indian History whose contributions to mathematics, science and astronomy are so stunning and advanced for his time and yet he has not been accorded the recognition in the world history of science. If he had been alive today he might have won a Nobel Prize or two! I have immense pride in bringing him to the attention of Indians and non-Indians alike.

At the age of 23 Aryabhata wrote his famed “Aryabhatiya”, the only one of 3 text books in Astronomy that survived. Approximately 1/3 of this text is devoted to mathematics; this spanned arithmetics, algebra, plane trigonometry and spherical trigonometry. A partial list of Aryabhata’s inventions and discoveries is given below:

### A: MATHEMATICS:

i) Aryabhata was aware of the concept of zero, as well as the use of large numbers up to 10^{18. }

ii) He is credited with inventing the ingenious place value system. The fact that Aryabhata was familiar with both zero and the place value system was addressed by the Arabic scholar Ifrah. He wrote: *It is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place value system; secondly, he carries out calculations on square and cubic roots which are impossible if numbers in question are not written according to the place value system and zero".*

iii) Aryabhata was the first to calculate the value for ‘pi’ accurately to the fourth decimal point; he described how he derived the value as follows:

"Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule, the relation of the circumference to diameter is known".

To summarize: 4+100 =104

104(8) = 832

62,000+832 = 62,832

If diameter is = 20,000, circumference is 62,832

This gives the value of pi = 62,832/20,000 = 3.1416 (the correct value to 8th place is 3.14159265).

iv) Aryabhata devised the formula for calculating areas of triangles, circles and cubes.

v) Solving the Pure Cubic: Aryabhata described his way as follows:

"One should divide the second aghana by three times the square of the cube roots of the preceding aghana. The square (of the quotient) multiplied by three times the purva (that part of the cube root already found) is to be subtracted from the first aghana and the cube (of the quotient of the above division) is to be subtracted from the aghana"

For a detailed description of the steps involved in this method, the reader is directed to www.math.sfu.ca/histmath/India/5th CenturyAD/purecubic.html

vi) In trigonometry, Aryabhata gave tables of sines calculating the approximate values at intervals of 90/24=3.45. For arriving at this value, he used the formula sin(n+1)x-sin nx. He was the first to use versine (1-cosine).

### B: ASTRONOMY:

i) Aryabhata determined that the earth was spherical and with the circumference of 24,835 miles (39,967 km), which is an excellent approximation.

ii) He suggested that the apparent rotation of the heavens was due to the axial rotation of the earth on its axis. Thus, he predated Copernicus by over a Millennium, and yet, the latter had been credited for this discovery by Western astronomers!

ii) He calculated the Astronomical ratio by dividing the 1,582,237,500 rotations of the Earth by 57,753,336 lunar orbits (1,582,237,500/57,753,336 = 27.396493572). This is an extremely accurate value of a fundamental astronomical ratio accepted by the authorities. This is the first astronomical constant described in history.

iii) Aryabhata was the first astronomer to devise a continuous counting of solar days, designating each day with a number; this count of days is termed “ahargana”.

iv) He correctly asserted that the planets shine due to the reflection of sunlight and that the eclipses occur due to the shadows of moon and earth. These are astounding observations as the Indians up to his time believed that eclipses were caused by a demon called “Rahu”!

v) Many of the above observations are truly spectacular and advanced for his age as they already discount the “flat earth” concept and lay the foundation for the belief that earth and other planets orbit the sun.

vi) Aryabhata correctly deduced that the orbits of the planets are ellipses; this is another stunning discovery not credited to him but to an European, ,Johannes Kepler (a German astronomer, born AD 1571).

vii) He suggested that the new day starts at midnight (rather than at sunrise)

### BIBLIOGRAPHY:

1) For a suitable list of books and articles on Aryabhata, please access the following internet site:

http://www-gap.dcs.st-and.ac.uk/~history/References/Aryabhata_I.html

2) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata-I.html

3) http://en.wikipedia.org/wiki/Aryabhata

4) http://www.math.sfu.ca/histmath/India/5thCenturyAD/Aryabhata.html

5) http://www.math.sfu.ca/histmath/India/5thCenturyAD/pi.html