Farkas Bolyai (February 9, 1775 - November 20, 1856, also known as Wolfgang Bolyai in Germany) was a Hungarian mathematician, mainly known for his work in Geometry. Image File history File links from http://www. ... Image File history File links from http://www. ... February 9 is the 40th day of the year in the Gregorian Calendar. ... 1775 was a common year starting on Sunday (see link for calendar). ... November 20 is the 324th day of the year (325th in leap years) in the Gregorian Calendar. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... Geometry (from the Greek words Geo = earth and metro = measure) is the branch of mathematics first popularized in ancient Greek culture by Thales (circa 624-547 BC) dealing with spatial relationships. ...

Biography

Bolyai was born in Bolya (Buia), a town near Nagyszeben (today Sibiu) in Transsylvania. Farkas was taught at home by his father until the age of six years when he was sent to the Calvinist school in Nagyszeben. His teachers immediately recognised his talents in arithmetics and in learning languages. With 12 years he left school and was appointed as a tutor to the eight year old son of the count Kemény. This meant that Bolyai was now treated as a member of one of the leading families in the country, and he became not only a tutor but a real friend to the count's son. In 1790 Bolyai and his pupil both entered the Calvinist College in Kolozsvár (Cluj-Napoca) where they spent five years. Sibiu (Hungarian: Nagyszeben, German: Hermannstadt) is a city in Transylvania, Romania with a population of 170,000. ... Transylvania (Romanian: Transilvania or Ardeal, Hungarian: Erdély, German: Siebenbürgen, Serbian: Transilvanija, Turkish: Erdel, Slovak: Sedmohradsko, Polish: Siedmiogród) is a historic region that forms the western and the central parts of Romania. ... In an unadorned church, the 17th century congregation stands to hear the sermon. ... A count is a nobleman in most European countries, equivalent in rank to a British earl, whose wife is still a countess (for lack of an Anglo-Saxon term). ... 1790 was a common year starting on Friday (see link for calendar). ... Map of Romania showing Cluj_Napoca Cluj_Napoca (Hungarian: Kolozsvár, German: Klausenburg, Latin: Claudiopolis), the seat of Cluj county, is one of the most important academic, cultural and industrial centers in Romania. ...

The professor of philosophy at the College in Kolozsvár tried to turn Bolyai against mathematics and towards religious philosophy. Bolyai, however, decided to go abroad with Simon Kemény on an educational trip in 1796 and began to study mathematics systematically at German universities first in Jena and then in Göttingen. Map of Germany showing Jena Jena is a town in central Germany on the River Saale. ... Landmark Gänseliesel fountain at the main market Göttingen (   listen?) is a city in Lower Saxony, Germany. ...

He returned home to Kolozsvár and later to Marosvásárhely (Târgu Mureş) in 1799. It was there he met and married Zsuzsanna Benkö and where their son János Bolyai - later an even more famous mathematician than his father - was born in 1802. T rgu Mureş (Hungarian: Marosv rhely, German: Neumarkt) is a city in Mureş county, Transylvania, Romania, with a population of 149,000, more than 40% of whom are ethnic Hungarians. ... 1799 was a common year starting on Tuesday (see link for calendar). ... János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician. ... 1802 was a common year starting on Friday (see link for calendar). ...

Mathematical work

Bolyai's main interests were the foundations of geometry and the parallel axiom. Geometry (from the Greek words Geo = earth and metro = measure) is the branch of mathematics first popularized in ancient Greek culture by Thales (circa 624-547 BC) dealing with spatial relationships. ... The term Parallel has a number of important meanings: Parallel (geometry) occurs in geometry. ... In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ...

His main work, the Tentamen, was an attempt at a rigorous and systematic foundation of geometry, arithmetic, algebra and analysis. In this work, he gave iterative procedures to solve equations which he then proved convergent by showing them to be monotonically increasing and bounded above. His study of the convergence of series includes a test equivalent to Raabe's test, which he discovered independently and at about the same time as Raabe. Other important ideas in the work include a general definition of a function and a definition of an equality between two plane figures if they can both be divided into a finite equal number of pairwise congruent pieces. Iteration is the repetition of a process, typically within a computer program. ... Convergence means approaching a definite value, as time goes on; or approaching a definite point, or a common view or opinion, or a fixed state of affairs. ... Plane may refer to: Look up Plane in Wiktionary, the free dictionary An Aeroplane or airplane, a type of fixed-wing aircraft. ... See also: congruence relation In geometry, two shapes are called congruent if one can be transformed into the other by a series of translations, rotations and reflections. ...

He first dissuaded his son from the study of non-Euclidean geometry, but by 1830 he became enthusiastic enough to persuade his son to publish his way-breaking thoughts. The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ...

External links

• Extensive biography
• Further references on Farkas Bolyai