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which his commentator Bhskara I (629 AD) identifies with Pāṭaliputra (modern Patna).
His book, the Āryabhatiya, presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun (in other words, it was heliocentric). This book is divided into four chapters: (i) the astronomical constants and the sine table (ii) mathematics required for computations (iii) division of time and rules for computing the longitudes of planets using eccentrics and epicycles (iv) the armillary sphere, rules relating to problems of trigonometry and the computation of eclipses. In this book, the day was reckoned from one sunrise to the next, whereas in his Āryabhata-siddhānta he took the day from one midnight to another. There was also difference in some astronomical parameters.
Āryabhata wrote that 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits. This is an extremely accurate ratio of a fundamental astronomical ratio (1,582,237,500/57,753,336 = 27.3964693572), and is perhaps the oldest astronomical constant calculated to such accuracy.
Aryabhata also gave an accurate approximation for π. In the Aryabhatiya, he wrote: "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." In other words, π ≈ 62832/20000 = 3.1416, correct to four rounded-off decimal places.
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Aryabhatta Aryabhatta Aryabhata