Al-Mahani

Abu 'Abd Allah Muhammad ibn 'Isa al-Mahani (c. 820 – c. 880/888) was a Persian mathematician and astronomer of the Islamic Golden Age. He was born in Mahan, a city in the Kerman province of Persia.

Al-Mahani is best known for his work on Archimedes' On the Sphere and Cylinder. He attempted to solve the problem of dividing a sphere by a plane into two segments whose volumes are in a given ratio. This problem leads to a cubic equation, and al-Mahani showed that the equation cannot be solved by ruler and compass constructions. His work on this problem represents a significant contribution to the theory of cubic equations. He also made contributions to the study of irrational ratios and their properties.

In astronomy, Al-Mahani made observations of lunar and solar eclipses. These observations were later used by Ibn Yunus. He also contributed to the refinement of astronomical instruments.

While many of his works are lost, fragments of his commentaries on Euclid's Elements and Menelaus of Alexandria's Spherics have survived. His work demonstrates a deep understanding of Greek mathematics and a dedication to extending and refining its principles.