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Aryabhata is the author of several treatises on mathematics and astronomy, though Aryabhatiya is the only one which survives. [16] Much of the research included subjects in astronomy, mathematics, physics, biology, medicine, and other fields. [17]
Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions.
Āryabhaṭa's table was the first sine table ever constructed in the history of mathematics. [8] The now lost tables of Hipparchus (c. 190 BC – c. 120 BC) and Menelaus (c. 70–140 CE) and those of Ptolemy (c. AD 90 – c. 168) were all tables of chords and not of half-chords. [8] Āryabhaṭa's table remained as the standard sine table of ...
He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapariksakrama is a manual on making observations in astronomy based on instruments of the time.
Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations.A linear Diophantine equation is an equation of the form ax + by = c where x and y are unknown quantities and a, b, and c are known quantities with integer values.
Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's ...
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Aryabhata II also deduced a method to calculate the cube root of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they played a vital role to calculate the planetary positions as accurately as possible.