Khayyam's quadrilateral and the parallel postulate
Crítica del quinto postulado: cuadrilátero de Jayam
- Date
- 1077 · confidence high
- Place
- Isfahan, Iran
- Credited to
- Omar Khayyam
- People
- 👤 Omar Jayam1048–1131
- Field
- Knowledge & symbols
What was discovered
In his commentary on Euclid he studies a quadrilateral with two equal sides perpendicular to the base and examines the hypotheses of acute, right or obtuse angles at the top. It is the same approach later taken up by al-Tusi and Saccheri, leading to non-Euclidean geometry.
In the West it is known as Saccheri's quadrilateral; the version by Nasir al-Din al-Tusi, published in Rome in 1594, may have reached Wallis and Saccheri.
What it led to
- al-Tusi's attempts to prove the postulate
- Saccheri's quadrilateral (1733)
- non-Euclidean geometries