Astronomy
Aryabhata I [b. India, 476 ce, d. India, 550] writes the Aryabhatiya. In it he recalculates Greek measurements of the solar system, obtaining a nearly correct value for Earth's circumference. Although he mostly accepts Ptolemy's scheme of the universe, he also puts forward the idea that Earth rotates and that the orbits of the planets are ellipses. He believes that the Moon and planets shine by reflected sunlight and gives correct explanations for eclipses. See also 240 bce Earth science.
MathematicsAryabhata, in the Aryabhatiya, includes a good value of 3.1416 for the ratio of a circle's circumference to its diameter and uses the decimal and place-value numeration system. His book also contains a variety of rules for algebra and for plane and spherical trigonometry, not all of them correct. Aryabhata also solves some Diophantine equations. See also 250 ce Mathematics.
Eutocius [b. Palestine, c. 480 ce, d. c. 540] writes the first of three commentaries on the works of Archimedes and one on the works of Apollonius. These remain the best source to this day of some of their mathematics.
