Mnemonics in trigonometry

Mehmet Nadir Bey, with daughter Hadiye

Mehmet Nadir (1856–1927) was a Turkish mathematician and educationist

Early life

He was born in Sakız island (modern Chios in Greece) then a part of the Ottoman Empire, to a poor family. He was adopted by a sea captain (who’d be his father in law in the future). He studied in the military high school in Bursa. Then he came to İstanbul to study in military collage and then the naval academy. After completing his education with honours, he was appointed as the mathematics teacher of the naval academy and then Darüşşafaka High School, one of the most prominent schools in İstanbul. In 1879, together with one of his friends he travelled to England for advanced studies. But the details of this period are not known. Probably, he also spent some time in Cyprus.

Educationist

After returning to İstanbul, he began teaching in private high schools and in 1884 he established a high school of his own. It was a junior high school ( Rüştiye). But later he added senior high school section to his school (İdadi) . Although there were private junior high schools before 1884, he was the founder of the very first private senior high school in İstanbul. This school is now considered as the core of the modern Istanbul High School for Boys (Template:Lang-tr). He also added a section for the girls and a branch school in Edirne. Another novelty he introduced was the first school newspaper in Istanbul.

Politics and later life

He secretly supported the Young Turks movement. But when the sultan Abdülhamit II arrested 350 Young Turk adherents on the charge of planning a coup in 1896, Mehmet Nadir was forced to resign. After working in a public school in İstanbul, in 1903 he was appointed to Aleppo (now in Syria) as the director of education. In 1908 Young Turks came to power and he was exiled to Tripoli (now in Libya) by the Young Turks who suspected of his betrayal back in 1896. After the Italo-Turkish War in which Italians invaded Libya he returned to İstanbul. Although he was also sent to Edirne, he soon returned to İstanbul during the Balkan Wars. After he convinced Young Turks of his innocence, he was appointed as the mathematics professor in the newly established Girls' University in İstanbul. In 1919 soon after the World War I he began working in the Darülfünun (present day, İstanbul University) as a müderris (professor) of mathematics in the newly established branch of Number theory. He died on 27 December 1927.

As a mathematician

Mehmet Nadir is considered as one of the first mathematicians of Turkey. He actively participated in a group of mathematicians of a French mathematics periodical named I’Intermediaire des Mathematiciens. According to Professor Erdal İnönü, total number of his messages to the periodical was 62. One example cited by Erdal İnönü is as follows The whole number solution to the equation

$x^2+y^2-z^2=u^5$

proposed by Mehmet Nadir is

$x=b\cdot (a^2+b^2)\cdot (a^2-b^2)$

$y=\frac{1}{2}\cdot ((a^2-1)\cdot (a^2+b^2{)}^2-4\cdot b^2)$

$z=\frac{1}{2}\cdot ((a^2+1)\cdot (a^2+b^2{)}^2+4\cdot b^2)$

$u=a^2+b^2$

where b is a pozitive integer and a is a positive odd integer.

In 1917 Mehmet Nadir published a book about the Number theory. In this book he proposed an alternative algorithm on divisibility. Felix Klein, well known German mathematics professor congratulated him for the algorithm.