Article ID: CBB000931404

Salih Zeki's Articles on the Trisection of an Angle (2005)

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Bir, Atilla (Author)
Kaçar, Mustafa (Author)


Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
Volume: 7, no. 1
Issue: 1
Pages: 45-66


Publication Date: 2005
Edition Details: [Translated title.] In Turkish.
Language: English

Trisecting an angle by using geometric methods and tools (a ruler and a pair of compass only) is an ancient problem which was desperately attempted over 2500 years. We know since Newton that this problem can not be solved by recourse to geometry, except for particular angle degrees. Throughout centuries, however, several amateur mathematicians claimed to have found a complete geometric solution. In a series of articles titled "A geometry problem concerning the trisection of an angle" published in Resimli Mecmua in 1891-1892, Salih Zeki discussed the problem in detail. He gave the main proofs concerning the trisection and showed why proposed solutions are not geometric. Furthermore, he discussed the proofs given by Masdariyecizade Hüseyin Efendi, teacher of mathematics at the Mühendishane-i Berri Humayun (Imperial School of Engineering). Hüseyin Efendi, arguing that he found a solution in 1823, had asked a commission of mathematicians to confirm it. While discussing Hüseyin Efendi's solution, Salih Zeki also referred to the work of a the Ottoman mathematician Vidinli Hüseyin Tevfik Pasa (1832-1901) and his book entitled Linear Algebra (Istanbul 1882, 1892) on the quaternions. Key words: Salih Zeki, history of mathematics, trisection of an angle, Resimli Gazete; Anahtar Kelimeler: Salih Zeki, matematik tarihi, açinin üçe bölünmesi, Resimli Gazete.

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Authors & Contributors
Vitrac, Bernard
Lorenat, Jemma
Terdimou, Maria
Netz, Reviel
Nauenberg, Michael
Maanen, Jan A. van
Journals
Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
Historia Mathematica
British Society for the History of Mathematics Bulletin
American Mathematical Monthly
Almagest
Neusis: The Greek Journal for the History and Philosophy of Science and Technology
Publishers
Harvard University
Concepts
Mathematics
Proof
Geometry
Linguistics; philology
Science and society
Diagrams
People
Ekinci, Salih Zeki
Heiberg, Johan Ludvig
Euclid
Liu, Yi
Steiner, Jakob
Schönemann, Theodor
Time Periods
19th century
Ancient
18th century
20th century, early
17th century
Renaissance
Places
Ottoman Empire
Greece
Denmark
Turkey
Netherlands
Italy
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