Aryabhata: A Genoius Mathematician and Astronomer

Aryabhata was born at Kusumapura (now Patna), India in 476.Although some believe that Aryabhata was born in South India, Kerala or Tamilnadu or Andra Pradesh. There are other conjectures also. We should not worry about all those conjecture as it is proved that he is an Indian.

At the age of 23 he wrote a small astronomical treatise, a masterpiece Aryabhatiya. In it he organized and combined existing knowledge of astronomy and mathematics. He says, "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”. There are 118 verses giving a summary of Hindu mathematics up to that time. Its mathematical section contains 33 verses giving 66 mathematical rules without proof. The Aryabhatiya contains an introduction of 10 verses, followed by a section on mathematics with, as we just mentioned, 33 verses, then a section of 25 verses on the reckoning of time and planetary models, with the final section of 50 verses being on the sphere and eclipses. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. In the algebra part Aryabhata tries to find out the solution the indeterminate equations of first degree by Kuttaka method i.e to find the integer solution of the equations of the form by = ax + c and by = ax - c, where a, b, c are integers.

The other contributions of Aryabhata were his appoximation of π and the sines tables. He wrote in the Aryabhatiya the following: - 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 given. This gives π = ⁶²⁸³²/₂₀₀₀₀ = 3.1416 which is a surprisingly accurate value. The trigonometry contained in Aryabhata's treatise gave a table of sines calculating the approximate values at intervals of 90/24 = 3 45'. Aryabhata also give the rule for summing the first n integers, the squares of these integers and also their cubes. Aryabhata gives formulae for the areas of a triangle and of a circle, which are correct, but the formulae for the volumes of a sphere and of a pyramid are claimed to be wrong by most historians. Aryabhata gave the curcumferrence of the Earth as 4 967 yojanas. Since 1 yojana = 5 miles this gives the circumference as 24 835 miles, currently the accepted value of curcumeferrence is 24 902 miles. Aryabhata gave an excellent appoximation. He mentioned that that the diurnal motion of the heavens is due to the rotation of the earth about its axis.

Aryabhata 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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