Salih Zeki's articles on the trisection of an angle

Year 2005, Volume: 7 Issue: 1, 45 - 66, 01.12.2005

Atilla Bir Mustafa Kaçar

Abstract

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 Paşa (1832-1901) and his book entitled
Linear Algebra (Istanbul 1882, 1892) on the quaternions. 

Keywords

Salih Zeki, history of mathematics, trisection of an angle, Resimli Gazete

Salih Zeki’nin ‘Teslis-i Zaviye’ Konusundaki “Bir Hendese Meselesi” Adlı Yazı Dizisi

Abstract

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 Paşa (1832-1901) and his book entitled Linear Algebra (Istanbul 1882, 1892) on the quaternions. 

Keywords

Salih Zeki, matematik tarihi, açının üçe bölünmesi, Resimli Gazete

References

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