Bolyai duels
- •
János Bolyai
Hungarian mathematician (1802–1860)
"Bolyai" redirects here. For the lunar crater, see Bolyai (crater).
The native form of this personal name is Bolyai János. This article uses Western name order when mentioning individuals.
János Bolyai (;[2]Hungarian:[ˈjaːnoʃˈboːjɒi]; 15 December 1802 – 27 January 1860) or Johann Bolyai,[3] was a Hungarianmathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.[4]
Early life
Bolyai was born in the town of Kolozsvár, Grand Principality of Transylvania (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.
By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. He
- •
Biography
Farkas Bolyai's mother was Krisztina Pávai Vajna and she inherited a small farm at Domáld which was near Marosvásárhely in Transylvania. Today Marosvásárhely is called Târgu-Mureș and is the capital of Mureș judet (county) situated in north-central Romania. Farkas Bolyai's father Gáspár Bolyai was 43 years old when Farkas was born. He came from a family with a long history of fighting against the Turkish invaders and his ancestors had been wealthy, but although Gáspár still owned a small estate at Bolya near Nagyszeben, the family were by this time no longer wealthy. Today Nagyszeben is called Sibiu and is the capital of Sibiu judet (county) situated in central Romania. When Farkas was born Nagyszeben was the military centre of Transylvania and the capital of the region.Farkas was taught at home by his father until he reached the age of six years when he was sent to the Calvinist school in Nagyszeben. His teachers immediately recognised his talents both in arithmetical calculation and in learning languages. When he was twelve years old he left school and was appoi
- •
Biography
János Bolyai's parents were Zsuzsanna Benkö, from Kolozsvár, and Farkas Bolyai, from Bolya (near Nagyszeben). János was born in Zsuzsanna's parents home in Kolozsvár (now renamed Cluj in Romania) but soon went to Marosvásárhely where his father Farkas had a job at the Calvinist College teaching mathematics, physics and chemistry. Farkas Bolyai always wanted his son to be a mathematician, and he brought him up with this in mind. One might suppose that this would mean that János's education was put first in the Bolyai household, but this was not so for Farkas believed that a sound mind could only achieve great things if it was in a sound healthy body, so in his early years most attention was paid to János's physical development. It was clear from early on, however, that János was an extremely bright and observant child [7]:-... when he was four he could distinguish certain geometrical figures, knew about the sine function, and could identify the best known constellations. By the time he was five [he] had learnt, practically by himself, to read. He was well above the a
Copyright ©hubdebt.pages.dev 2025