Salih Zeki's articles on the trisection of an angle

Atilla Bir, Mustafa Kaçar

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.

Key words: Salih Zeki, history of mathematics, trisection of an angle, Resimli Gazete; Anahtar Kelimeler: Salih Zeki, matematik tarihi, açının üçe bölünmesi, Resimli Gazete.