planetary theory, and solutions to determine the direction of Qibla. Mathematics He defined the tangent function, and he established several trigonometric identities in their modern form, where the ancient Greek mathematicians had expressed the equivalent identities in terms of chords. The trigonometric identities he introduced were: He may have developed the law of sines for spherical triangles, though others like Abu-Mahmud Khojandi have been credited with the same achievement: where are the sides of the triangle (measured in radians on the unit sphere) and are the opposing angles. Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi. Works Almagest ( Kitāb al-Majisṭī). A book of zij called Zīj al‐wāḍiḥ (), no longer extant. "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", ( Kitāb fī mā yaḥtāj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya). This text contains over one hundred geometric constructions, including for a regular heptagon, which have been reviewed and compared with other mathematical treatises. The legacy of this text in Latin Europe is still debated. "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", ( Kitāb fī mā yaḥtāj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb). This is the first book where negative numbers have been used in the medieval Islamic texts. He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements. Legacy The crater Abul Wáfa on the Moon is named after him. On 10 June 2015, Google changed its logo in memory of Abu al-Wafa' Buzjani. Notes References (PDF version) (PDF version) External links 10th-century Iranian mathematicians People from Torbat-e Jam 940 births 998 deaths Scientists who worked on qibla determination 10th-century Iranian astronomers Mathematicians from Nishapur Scholars under the Buyid dynasty