János Bolyai (1802-1860) Hungarian mathematician (artwork made by Attila Zsigmond)

Memorial plaque of János Bolyai in Olomouc, (Czech Republic). Olomouc (ˈolomoʊ̯ts ( local Haná dialect Olomóc or Holomóc, German Olmütz, Polish Ołomuniec, Latin The Czech Republic ( ˈt͡ʃɛskaː ˈrɛpuˌblɪka short form in Česko ˈt͡ʃɛskɔ also called Czechia,

János Bolyai (December 15, 1802 – January 27, 1860) was a Hungarian mathematician, known for his work in non-Euclidean geometry. Events 533 - Byzantine general Belisarius defeats the Vandals, commanded by King Gelimer, at the Battle of Year 1802 ( MDCCCII) was a Common year starting on Friday of the Gregorian calendar or a Common year starting on Wednesday of the Events 98 - Trajan becomes Roman Emperor after the death of Nerva. Year 1860 ( MDCCLX) was a Leap year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Leap year starting Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic A mathematician is a person whose primary area of study and research is the field of Mathematics. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry

Bolyai was born in Kolozsvár, Transylvania (today Cluj-Napoca, Romania), the son of a well-known mathematician, Farkas Bolyai. (pronunciation in Romanian: /'kluʒ na'poka/ Klausenburg Kolozsvár Napoca Castrum Clus Claudiopolis קלויזנבורג Kloiznburg until 1974 Cluj, is the third Transylvania (Ardeal or ro ''Transilvania'' Erdély, see also other denominations) is a Central European region located in the eastern half of the Carpathian (pronunciation in Romanian: /'kluʒ na'poka/ Klausenburg Kolozsvár Napoca Castrum Clus Claudiopolis קלויזנבורג Kloiznburg until 1974 Cluj, is the third Romania ( dated: Rumania, Roumania Farkas Bolyai ( February 9, 1775 - November 20, 1856, also known as Wolfgang Bolyai in Germany was a Hungarian mathematician

By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Analytical mechanics is a term used for a refined highly mathematical form of Classical mechanics, constructed from the Eighteenth century onwards as a formulation He studied at the Royal Engineering College in Vienna from 1818 to 1822. Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. Year 1818 ( MDCCCXVIII) was a Common year starting on Thursday (link will display the full calendar of the Gregorian Calendar (or a Common Year 1822 (MDCCCXXII was a Common year starting on Tuesday (see link for calendar of the Gregorian calendar (or a Common year starting on Sunday of the He became so obsessed with Euclid's parallel postulate that his father wrote to him: "For God's sake, I beseech you, give it up. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive Fear it no less than sensual passions because it too may take all your time and deprive you of your health, peace of mind and happiness in life". János, however, persisted in his quest and eventually came to the conclusion that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on its negation. He wrote to his father: "Out of nothing I have created a strange new universe". ^[1] Between 1820 and 1823 he prepared a treatise on a complete system of non-Euclidean geometry. Year 1820 ( MDCCCXX) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a Leap year Year 1823 ( MDCCCXXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian Calendar (or a Common In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father. Year 1832 ( MDCCCXXXII) was a Leap year starting on Sunday (link will display the full calendar of the Gregorian

Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order". Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German A geometer is a Mathematician whose area of study is Geometry. In 1848 Bolyai discovered not only that Lobachevsky had published a similar piece of work in 1829, but also a generalisation of this theory. Year 1848 ( MDCCCXLVIII) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap Nikolai Ivanovich Lobachevsky (Никола́й Ива́нович Лобаче́вский ( December 1 1792 &ndash February 24 1856 ( N For the game see 1829 (board game. Year 1829 ( MDCCCXXIX) was a Common year starting on Thursday (link will display Generalization is a foundational element of Logic and human reasoning. As far as we know, Lobachevsky published his work a few years earlier than Bolyai, but it contained only hyperbolic geometry. Bolyai and Lobachevsky didn't know each other or each other's works.

In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted In Mathematics, the real numbers may be described informally in several different ways Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died. These can now be found in the Bolyai-Teleki library in Târgu-Mureş, Romania, where Bolyai died. Târgu Mureş (ˈtɨrgu ˈmureʃ in Romanian; Târgu Mureş Marosvásárhely (Székely-Vásárhely Neumarkt am Mieresch Novum Forum Siculorum is a city in Mureş

He was an accomplished polyglot speaking nine foreign languages, including Chinese and Tibetan. A language is a dynamic set of visual auditory or tactile Symbols of Communication and the elements used to manipulate them Tibetan refers to a group of languages spoken primarily by Tibetan peoples who live across a wide area of eastern Central Asia bordering South Asia as well as by overseas

No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.

Legacy

Unauthentic portrait of Bolyai

The Babeş-Bolyai University in Cluj-Napoca bears his name, as does the Bolyai crater on the Moon [1]. The Babeş-Bolyai University (UBB—Universitatea Babeş-Bolyai in Cluj-Napoca is the largest University in Romania. Bolyai is an old lunar crater that is located in the southern hemisphere on the far side of the Moon. Also, in the Carpathian basin, many high schools bear his name. The Pannonian Basin or Carpathian Basin is a large basin in Central Europe.

References

External links

• O'Connor, John J. & Robertson, Edmund F. , “János Bolyai”, MacTutor History of Mathematics archive 
• János Bolyai at the Mathematics Genealogy Project