Spherical law of sines (Ibn Iraq)
Ley de los senos esférica (Ibn Iraq)
- Date
- c. 1000 (discutido) · confidence low
- Place
- Kath (present-day Beruniy), Khwarazm, Uzbekistan
- Credited to
- Abu Nasr Mansur ibn Iraq (also claimed for al-Khujandi and Abu al-Wafa)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A formula relating the sines of the sides of a spherical triangle to those of the opposite angles, used to solve astronomy and qibla problems on a sphere. It is attributed, among others, to Ibn Iraq, al-Biruni's teacher.
Priority is disputed between Ibn Iraq (Khwarazm), Abu Mahmud al-Khujandi (Rayy) and Abu al-Wafa (Baghdad), who worked in the same decade; the dating is approximate and there is no agreement on who first formulated it.
What it led to
- spherical trigonometry independent of astronomy (Nasir al-Din al-Tusi)
- calculation of the qibla from any place
- European trigonometry of the 13th-15th centuries