Two spinning circles invented by Nasir al-Din al-Tusi reappeared in Copernicus
In the 13th century a Persian scholar showed that two circles rolling one inside the other can produce motion in a straight line. The trick let Nasir al-Din al-Tusi drop an awkward device from Ptolemy's astronomy, and nearly three centuries later the same geometry turned up in the work of Nicolaus Copernicus.
Tusi was born in 1201 in Tus, in Khorasan in northeastern Iran, into a Shia family, and lost his father young. Honouring his father's wishes, he travelled widely for teachers, studying philosophy and mathematics in Nishapur and astronomy in Mosul. Among those he met was the Sufi poet Attar. He would eventually write around 150 works, most in Arabic and about 25 in Persian, including standard Arabic editions of Euclid, Archimedes and Ptolemy.
His career was shaped by the Mongol invasions. While Mongol armies under Genghis Khan overran Khorasan, he found work with the Nizari Ismaili state, moving between mountain castles such as Alamut. When Hulegu, Genghis Khan's grandson, took those strongholds in 1256, he made Tusi a scientific adviser. Tusi's role in the Mongol sack of Baghdad in 1258 remains controversial. Afterwards he oversaw religious endowments and is credited with protecting libraries and schools.
He talked Hulegu into funding an observatory at Maragheh, begun in 1259 and among the most advanced of its day. The resulting Ilkhanic Tables of 1272 tracked planetary positions with great accuracy. His Tusi couple replaced Ptolemy's troublesome equant for most planets, though Mercury defeated him. He questioned whether Ptolemy's evidence really proved the Earth stood still, arguments that echo in Copernicus. He also suggested that the Milky Way was a dense crowd of tiny stars, something Galileo's telescope confirmed in 1610.
Mathematicians remember him for freeing trigonometry from astronomy. His treatise on the quadrilateral treated spherical trigonometry as a subject in its own right and was the first to set out the six cases of a right spherical triangle. The historian Ibn Khaldun judged him the greatest of the later non-Arab scholars. Tusi died in 1274.
Source: Nasir al-Din al-Tusi
