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Person: Al-Khujandi, Abu Mahmud Hamid ibn al-Khidr

Al-Khujandi was an Islamic astronomer and mathematician. He made accurate astronomical observations and may have made some advances in trigonometry.

Mathematical Profile (Excerpt):

• From al-Tusi's comments we can be fairly certain that al-Khujandi came from the city of Khujand.
• Al-Tusi says that al-Khujandi was one of the rulers of the Mongol tribe in that region so he must have come from the nobility.
• Al-Khujandi was supported in his scientific work for most of his life by members of the Buyid dynasty.
• Al-Khujandi received patronage from Fakhr ad-Dawlah who ruled from 976 to 997.
• It was Fakhr ad-Dawlah who supported al-Khujandi in his major project to construct a huge mural sextant for his observatory at Rayy, which is near modern Tehran.
• Al-Khujandi's mural sextant was his own invention and it did break new ground in having a scale which indicated seconds, a level of accuracy never before attempted.
• During the year 994 al-Khujandi used the very large instrument to observe a series of meridian transits of the sun near the solstices.
• There is, however, an error in al-Khujandi's value for the obliquity of the ecliptic; it is about two minutes too low.
• The error was discussed by al-Biruni in his Tahdid where he claimed that the aperture of the sextant settled about one span in the course of al-Khujandi's observations due to the weight of the instrument.
• However, al-Khujandi's latitude for Rayy, 35° 34' 38.45", despite being calculated using his erroneous value for the obliquity of the ecliptic, is accurate to the nearest minute of arc.
• It remains for us to discuss the claim that al-Khujandi discovered the sine theorem.
• The claim was made by al-Tusi who gives al-Khujandi's proof of the result for spherical triangles in his Shakl al-qatta.
• Although there is no reason to doubt al-Tusi that the proof he gives does indeed come from al-Khujandi there is quite a few reason to believe that one of Abu'l-Wafa or Abu Nasr Mansur was the original discoverer.
• Both Abu'l-Wafa and Abu Nasr Mansur claim to have discovered the sine theorem while, as far as we are aware, al-Khujandi makes no such claim.
• Also al-Khujandi was more of a designer of astronomical instruments and an astronomical observer than he was theoretician.
• We should make one final comment on the mathematical contributions of al-Khujandi.
• that what Abu Muhammad al-Khujandi advanced - may God have mercy on him - in his demonstration that the sum of two cubic numbers is not a cube, is defective and incorrect.
• It is certainly interesting that al-Khujandi, despite his practical rather than theoretical achievements, should be interested in this number theory result.

Born about 940, Khujand, Tajikistan. Died 1000.

View full biography at MacTutor

Tags relevant for this person:

Ancient Arab, Astronomy, Origin Tajikistan

Mentioned in:

Epochs: 1

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@J-J-O'Connor

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive