Aryabhata writes the Āryabhaṭīya at age 23, a treatise in 121 Sanskrit verses that systematizes arithmetic, algebra, plane and spherical trigonometry, and astronomy. He introduces sine tables (jyā), the value of π ≈ 3.1416 as an explicit approximation, and the second-order difference method for interpolating planetary positions. He proposes that the apparent rotation of the stars is due to Earth's rotation on its axis. Translated into Arabic c. 820 at Baghdad's House of Wisdom under the title Zīj al-Arjabhar, it directly influenced Al-Khwarizmi and the transmission of Indian mathematics to the Islamic and European worlds.