- Farkas Bolyai
Farkas Bolyai (
February 9 ,1775 -November 20 ,1856 , also known as Wolfgang Bolyai in Germany) was a Hungarian mathematician, mainly known for his work ingeometry .Biography
Bolyai was born in Bolya (
Buia ), a town near Nagyszeben (todaySibiu ) inTransylvania . Farkas was taught at home by his father until the age of six years when he was sent to theCalvinist 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 thecount 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.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 inGöttingen . In these times Bolyai became a close friend ofCarl Friedrich Gauss .He returned home to Kolozsvár 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. Soon thereafter he accepted a teaching position for mathematics and sciences at the Calvinist College in Marosvásárhely (Târgu-Mureş ), where he spent the rest of his life.Mathematical work
Bolyai's main interests were the foundations of
geometry and theparallel axiom .His main work, the "Tentamen" ("Tentamen iuventutem studiosam in elementa matheosos introducendi"), 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 theconvergence of series includes a test equivalent toRaabe'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 pairwisecongruent pieces.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.External links
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* [http://www-groups.dcs.st-and.ac.uk/~history/References/Bolyai_Farkas.html Further references on Farkas Bolyai]
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