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A generalisation of a theorem of al-Kuhi

Published online by Cambridge University Press:  12 November 2024

Sadi Abu-Saymeh  and
Mowaffaq Hajja
Sadi Abu-Saymeh
Affiliation:
2271 Barrowcliffe Dr., Concord, NC 28027, USA e-mail: [email protected]
Mowaffaq Hajja
Affiliation:
P. O. Box 388 (Al-Hoson), 21510 – Irbid – Jordan e-mail: [email protected], [email protected]
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Several problems that were composed and/or solved by the tenth century Islamic mathematician Abu Sahl al-Kuhi reached us via the writings of Abd al-Jalil al-Sijzi, another tenth century Islamic mathematician who, according to [1], was presumably a student of al-Kuhi’s. Twelve of these (sets of) problems and theorems are discussed in [1] and are referred to as The Fragments. The theorem of al-Kuhi alluded to in the title is Fragment #9, which is presented below, together with Fragment #5 and their proofs, in Section 2. Section 3 is devoted to the generalisation referred to in the title. Section 4 describes a relation to angle trisection and Sections 5 and 7 a relation too a configuration of Serenus. Section 6 contains a speculation on what motivated Fragment #9.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 573 , November 2024 , pp. 460 - 469
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

Berggren, J. Len and Hogendijk, Jan. P., The fragments of Abu Sahl al- Kuhi’s lost geometrical works in the writings of al-Sijzi, Suhail, 2 (2001), pp. 609–665.Google Scholar
Smith, Charles, Elementary treatise on conic sections, Macmillan, London (1904).Google Scholar
Thomas Little Heath, Apollonius of Perga: treatise on conic sections, Cambridge (1896).Google Scholar
Katz, Victor J., A history of mathematics: an introduction, Harper Collins1993.Google Scholar
Serenus d’Antinoë, Le Livre de la section du cylindre et le livre de la section du cône, translated by Paul Ver Ecke, Libraire Scientifique et Technique, Paris (1969).Google Scholar
Honsberger, Ross, Mathematical morsels, Mathematical Association of America, Washington, D. C. (1978).Google Scholar
Honsberger, Ross, Mathematical Gems III, Mathematical Association of America (1985).CrossRefGoogle Scholar
Hajja, Mowaffaq, Another morsel of Honsberger, Math. Mag. 83 (2010) pp. 279–283.CrossRefGoogle Scholar
Hajja, Mowaffaq, On a problem of Sastry and a theorem of Serenus, Math. Gaz. 103 (July 2019) pp. 328–332.CrossRefGoogle Scholar