Abu al-Wafa al-Buzjani

Abu al-Wafa al-Buzjani was a Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetic for businessmen contains the first instance of using negative numbers in a medieval Islamic text. He is also credited with compiling the tables of sines and tangents at 15' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc. His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived. He was born in Buzhgan, (now Torbat-e Jam) in Khorasan (in today's Iran). At age 19, in 959, he moved to Baghdad and remained there until his death in 998. ⁴ He was a contemporary of the distinguished scientists Abu Sahl al-Quhi and al-Sijzi who were in Baghdad at the time and others such as Abu Nasr Mansur, Abu-Mahmud Khojandi, Kushyar Gilani and al-Biruni. In Baghdad, he received patronage from members of the Buyid court. Abu al-Wafa was the first to build a wall quadrant to observe the sky. ⁶ It has been suggested that he was influenced by the works of al-Battani as the latter described a quadrant instrument in his Kitab az-Zij. ⁶ His use of the concept of the tangent helped solve problems involving right-angled spherical triangles. He developed a new technique to calculate sine tables, allowing him to construct more accurate tables than his predecessors. ⁷ In 997, he participated in an experiment to determine the difference in local time between his location, Baghdad, and that of al-Biruni (who was living in Kath, now a part of Uzbekistan). The result was very close to present-day calculations, showing a difference of approximately 1 hour between the two longitudes. Abu al-Wafa is also known to have worked with Abu Sahl al-Quhi, who was a famous maker of astronomical instruments. ⁷ While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni. ⁷ He translated and wrote commentaries, since lost, on the works of the Greek mathematicians Euclid and Diophantus of Alexandria and the Arabic mathematician al-Khwarizmi. Abu al-Wafa also wrote two (extant) works aimed at the practical user, Kitab fi ma yahutaj ilayhi al-kuttab wa'l-ummal min ilm al-hisab ("Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen") and Kitab fi ma yahutaj ilayhi al-sani min al-a'mal al-handasiyya ("Book on What Is Necessary from Geometric Constructions for the Artisan"). In honor of his astronomical work, a crater on the Moon was named for him.