Aryabhata wrote Aryabhatiya , finished in 499, which is a summary of Hindu mathematics up to that time, written in verse. It coveres astronomy, spherical trigonometry, arithmetic, algebra and plane trigonometry. Aryabhata gives formulas for the areas of a triangle and a circle which are correct, but the formulas for the volumes of a sphere and a pyramid are wrong.
Aryabhatiya also contains continued fractions, quadratic equations, sums of power series and a table of sines. Aryabhata gave an accurate approximation for (equivalent to 3.1416) and was one of the first known to use algebra. He also introduced the versine ( versin = 1 - cos) into trigonometry.
Aryabhata also wrote the astronomy text Siddhanta which taught that the apparent rotation of the heavens was due to the axial rotation of the Earth. The work is written in 121 stanzas. It gives a quite remarkable view of the nature of the solar system.
Aryabhata gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon.
His value for the length of the year at 365 days 6 hours 12 minutes 30 seconds is an overestimate since the true value is less than 365 days 6 hours.
References (32 books/articles)
References elsewhere in this archive:
Tell me about Aryabhata's contribution to trigonometry
There is a Crater Aryabhata on the moon. You can see a list of lunar features named after mathematicians.
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