What did Aryabhata work out about pi, the sine and a spinning Earth?

Aryabhata worked out three things that still echo. He taught that the Earth spins on its axis every day, he gave the sine the name that became our word for it, and he may even have suspected that pi is an irrational number. Aryabhata (476-550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and astronomy, and his Aryabhatiya mentions that in 499 CE he was 23 years old.

Start with the Earth. Aryabhata stated that the Earth is round and rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, contrary to the then-prevailing view that the sky rotated. He made it vivid: just as a man in a boat moving forward sees stationary objects on the shore moving backward, so the stationary stars are seen by people on Earth as moving towards the west.

His astronomy also explained eclipses scientifically. He stated that the Moon and planets shine by reflected sunlight, and explained eclipses as shadows cast by and falling on Earth, instead of the prevailing view that Rahu and Ketu cause them.

Then there is pi. Aryabhata worked on the approximation for pi and may have concluded that it is irrational: it is speculated that his word āsanna, "approaching", meant the value can never be written exactly. If so, that was a sophisticated insight, because Europe proved pi irrational only in 1761.

His mathematics left an everyday word behind. Aryabhata discussed the sine under the name ardha-jya, "half-chord". Arabic writers rendered it as jiba and later substituted jaib, meaning "pocket", and Gherardo of Cremona translated that into the Latin sinus, whence the English word sine. So the English word sine descends from a Sanskrit half-chord.

India's first satellite, Aryabhata, and a lunar crater are named in his honour.