Hasan Fehmi’s [Çayköy] Articles in Mathematics Published in Darülfünûn Fünûn Fakültesi Mecmuası [Darülfünûn Science Faculty Journal]
Müjdat TakıcakAfter graduating from the Mathematics Department of Darülfünun in 1911, Hasan Fehmi [Çayköy] worked as a mathematics teacher in distinguished high schools such as Kabataş High School, Mercan High School, Girls’ Teacher School and Darüşşafaka High School. Hasan Fehmi, who closely followed national and international scientific articles and had a close relationship with the teachers of the Mathematics Department, published articles in numerous journals such as Talebe Mecmuası, Riyaziyyat, and Darülfünûn Fünûn Fakültesi Mecmuası. As a teacher, it is noteworthy that he was so interested in scientific publications. Hasan Fehmi, one of the two teachers whose articles were published in the Darülfünûn Fünûn Fakültesi Mecmuası, was the fifth most published person, with six articles published between 1916 and 1917. The transliteration and mathematical evaluation of these articles, which were titled “Küre Hacminin Bi’l-Cebr İstihrâcı”, “Hendese Meselesi”, “Müsellesât [1]”, “Bir Gâye Meselesi”, “Müsellesât [2]” and “Cebir” respectively, were carried out within the scope of this study. According to the findings, these articles introduced and proved particular mathematical problems at the undergraduate level. These proofs used the basic rules of arithmetic and geometry, where no original approach was found.
Hasan Fehmi’nin [Çayköy] Darülfünûn Fünûn Fakültesi Mecmuası’nda Yayımlanan Matematik Makaleleri
Müjdat TakıcakHasan Fehmi [Çayköy] 1911 yılında Darülfünun Riyaziye Şubesi’nden mezun olduktan sonra, Kabataş Sultanisi, Mercan Sultanisi, Kız Muallim Mektebi, Darüşşafaka Lisesi gibi seçkin liselerde matematik öğretmenliği yapmıştır. Ulusal ve uluslararası bilimsel makaleleri yakından takip eden ve Riyaziye Şubesi hocaları ile yakın ilişkisi olan Hasan Fehmi, Talebe Mecmuası, Riyaziyyat ve Darülfünûn Fünûn Fakültesi Mecmuası gibi çok sayıda dergide makaleler yayımlamıştır. Bir öğretmen olarak bilimsel yayınlarla bu kadar ilgili olması dikkat çeken bir durumdur. Zira Darülfünûn Fünûn Fakültesi Mecmuası’nda makalesi yayımlanan iki öğretmenden biri olan Hasan Fehmi, 1916-1917 yılları arasında yayımladığı 6 makale ile en çok yayın yapan beşinci kişi olmuştur. İsimleri sırasıyla “Küre Hacminin Bi’l-Cebr İstihrâcı”, “Hendese Meselesi”, “Müsellesât [1]”, “Bir Gâye Meselesi”, “Müsellesât [2]” ve “Cebir” olan bu makalelerin transliterasyonu ve matematiksel değerlendirilmesi eldeki bu çalışma kapsamında yapılmıştır. Elde edilen bulgulara göre, söz konusu makalelerde lisans seviyesinde özel matematiksel problemler tanıtılmış ve ispatlanmıştır. Özgün bir yaklaşıma rastlanmayan bu ispatlarda aritmetiğin ve geometrinin temel kuralları kullanılmıştır.
In the nineteenth century, the Ottoman Empire was aware of its scientic deciency and while trying to solve it introduced numerous innovations in education. The Ottoman Empire wanted to bring Western science to the country by sending successful students to Western countries. During this period, many students completed their education, returned to the country, and contributed to the country’s academic media. This situation was also reflected in Darülfünun, and efforts were made to increase the qualifications of its faculties. One of these was the publication of a scientific journal called Darülfünûn Fünûn Fakültesi Mecmuası in 1916. After publishing six issues between 1916 and 1917, the journal went on a forced holiday due to the war. In this period, Hasan Fehmi [Çayköy] (1887-1950) published the highest number of articles in the field of mathematics in this journal. Hasan Fehmi, who graduated from Darülfünun’s Mathematics Department in 1911, worked as a mathematics teacher in the elite high schools of his time, such as Kabataş High School, Mercan High School, Girls’ School of Education, and Darüşşafaka High School. He was also the principal of Darüşşafaka between 1939 and 1943. Analyzing the articles in scientific periodicals published in the last period of the Ottoman Empire will contribute to the literature in this field. In this context, the present study aims to make a mathematical analysis of all of Hasan Fehmi’s articles published in Darülfünûn Fünûn Fakültesi Mecmuası. In this context, six articles by Hasan Fehmi published in the journal were transliterated, and mathematical analyses were made separately.
Between 1916 and 1917, Hasan Fehmi published 6 articles in the Darülfünûn Fünûn Fakültesi Mecmuası on mathematics. In his essays, he explained his subjects using a simple style and elaborately drawn figures at the necessary points.
In his first article, titled “Küre Hacminin Bi’l-Cebr İstihrâcı (Determination of Sphere Volume with Algebra)”, Hasan Fehmi used algebraic methods to determine how the expression 4/3πr³, which is the volume formula of any sphere with radius r, emerged.
In his second article, “Hendese Meselesi (Geometry Problem)”, Hasan Fehmi dealt with a problem concerning the relationship between a circle and a triangle. In the problem, any angle, such as XVY, is first drawn on the plane, and then points H and B are chosen on the arms of that angle such that VH + VB is constant. It is claimed that the circumcircles of the triangles VHB obtained from here will pass through a fixed point, and then the claim is proved.
In his third article, “Müsellesât [1] (Trigonometry [1])”, Hasan Fehmi explained the solution to a trigonometry problem based on the relationship between a circle and a triangle. In this problem, let the heights of a triangle such as BLC intersect at the point K and let M be the center of the circumcircle of the triangle. The necessary conditions for the line segment MK passing through K and M to be equal to half of the base of the triangle are analyzed in this problem.
In his fourth article, “Bir Gâye Meselesi (A Limit Problem)”, Hasan Fehmi examined whether the limit value of the sum 1x2/3x4x5x6 + 2x3/4x5x6x7 + ... + n(n+1)/(n+3)(n+4)(n+5) is equal to 1/9.
In his fifth article, “Müsellesât [2] (Trigonometry [2])”, Hasan Fehmi drew a line from a point G chosen randomly outside a triangle like BCE to the vertices of the triangle. The perpendicularity centers of the three new triangles obtained are K1 , K2 and K3 , respectively. In this problem, Hasan Fehmi showed the equality of the triangle K1 K2 K3 and the triangle BCE.
In his sixth article titled “Cebir (Algebra)”, Hasan Fehmi discussed the derivatives of some special trigonometric functions, the equality of the derivative values of these special functions to each other, and finally, the equality of the derivatives of these special functions without derivative operation.
Hasan Fehmi included some special problem situations and solutions in the fields of geometry, trigonometry, and algebra in his articles published in Darülfünûn Fünûn Fakültesi Mecmuası. Within the scope of the present study, these articles were analyzed mathematically in detail. According to the results obtained, it has been determined that the problems in question are at a level that can be accepted at the undergraduate level today and frequently brought up in the related courses. In this sense, they have a widespread recognition. In addition, the approaches used in problem-solving are not original. Hasan Fahmi does not make such a claim in his articles.
