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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: ssaymeh@yahoo.com
Mowaffaq Hajja
Affiliation:
P. O. Box 388 (Al-Hoson), 21510 – Irbid – Jordan e-mail: mowhajja@yahoo.com, mowhajja1234@gmail.com
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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

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