(Persian: محمد بن محمد بن الحسن طوسی*) (born 18 February 1201 in Ṭūs, Khorasan – died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad), better known as Nasīr al-Dīn Tūsī (Persian: نصیر الدین طوسی*; or simply Tusi in the West), was a Persian[1][2][3][4] polymath and prolific writer: an architect, astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, theologian and Marja Taqleed.[citation needed] He was of the Ismaili-, and subsequently Twelver Shī‘ah Islamic belief.[5] The Muslim scholar Ibn Khaldun (1332–1406) considered Tusi to be the greatest of the later Persian scholars.[6]
"Al-Tusi was the first to write a work on trigonometry independently of astronomy.[19] Al-Tusi, in his Treatise on the Quadrilateral, gave an extensive exposition of spherical trigonometry, distinct from astronomy.[20] It was in the works of Al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long.[21][22]
He was the first to list the six distinct cases of a right triangle in spherical trigonometry
In his On the Sector Figure, appears the famous law of sines for plane triangles.[23]
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
He also stated the law of sines for spherical triangles,[24][25] discovered the law of tangents for spherical triangles, and provided proofs for these laws.[23]
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