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Topic: Bolyai

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	Farkas Bolyai - Wikipedia, the free encyclopedia
		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.
		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.
		Bolyai's main interests were the foundations of geometry and the parallel axiom.
	en.wikipedia.org /wiki/Farkas_Bolyai (438 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		János Bolyai (December 15, 1802-January 27, 1860) was a Hungarian mathematician.
		Bolyai was born in Kolozsvar (today Cluj-Napoca in Romania), Transylvania, at that time part of the Austro-Hungarian Empire.
		Bolyai's work was published in 1832 as an Appendix to an essay by his father.
	wikiwhat.com /encyclopedia/j/ja/janos_bolyai.html (214 words)

	János Bolyai - Wikipedia, the free encyclopedia
		János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician.
		Bolyai was born in Kolozsvár, Transylvania (today Cluj-Napoca, Romania).
		Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father.
	en.wikipedia.org /wiki/J%C3%A1nos_Bolyai (339 words)

	BookRags: János Bolyai Biography
		The son of Farkas (Wolfgang) and Susanna Arkos Bolyai, Bolyai was born in Kolosvar, Transylvania, Hungary, on December 15, 1802.
		Bolyai was dismayed anew on publication--neither father or son had been aware that Lobachevsky had published a paper outlining the concepts of non-Euclidean geometrythree years before their work was issued.
		Bolyai continued to live at the family estate as a semi-recluse, and his occasional writings from 1856 to 1860 include a memorial to his mother and a lively appreciation of the ballet company at the Vienna Opera House.
	www.bookrags.com /biography/janos-bolyai-wom (885 words)

	Bolyai
		By the tender age of 13, Bolyai had developed a mastership of calculus and other sorts of analytical mathematics and mechanics.
		Mainly, Janos was taught by his father, Farkas Bolyai, who gave his son unparalleled instruction.
		Tormented by a horendous fever, Bolyai was pensioned from the army in 1833 and died on January 27, 1860.
	members.tripod.com /~noneuclidean/bolyai.html (308 words)

	FARKAS BOLYAI
		Bolyai on the other hand had wide ranging interests, science, mathematics, and literature all interested him and in 1795 after leaving the College he spent a few weeks considering a career as an actor.
		This meant that Bolyai was presented with its fundamental idea that reason was the route to understanding the universe and to improving the position of man. Knowledge, freedom, and happiness should be the aims of a rational human being.
		By the autumn of 1798 Bolyai and Kemény had completed their studies but back in Hungary Baron Kemény had hit hard times financially and although he supplied enough money for his son to return, Bolyai was left penniless in Göttingen.
	www.southernct.edu /~pinciuv/mat530pr9.html (2512 words)

	Bolyai, János
		Bolyai was born in Koloszvár, Hungary (now Cluj, Romania), and was taught mathematics by his father.
		By about 1820, János Bolyai had become convinced that a proof of Euclid's postulate about parallel lines was impossible; he began instead to construct a geometry which did not depend upon Euclid's axiom.
		This was a theory of absolute space in which several lines pass through the point P without intersecting the line L. He developed his formula relating the angle of parallelism of two lines with a term characterizing the line.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/B/BolyaiJ/1.html (225 words)

	Janos Bolyai, Euclid, and the Nature of Space - The MIT Press (Site not responding. Last check: 2007-11-01)
		As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twenty-four-page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry.
		Bolyai's "Appendix" (published as just that -- an appendix to a much longer mathematical work by his father) set up a series of mathematical proposals whose implications would blossom into the new field of non-Euclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp.
		In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition.
	mitpress.mit.edu /0262571749 (205 words)

	test (Site not responding. Last check: 2007-11-01)
		János Bolyai was born in Transylvania, which is now part of Romania (although at the time it was part of the Austro-Hungarian empire).
		Bolyai became interested in Euclidean geometry when he was first introduced to it as a teenager.
		Bolyai spent three years (1820 - 1823) working on non-Euclidean geometry only to discover that he had been pre-empted by Gauss before he managed to publish it.
	www.mathsyear2000.org /timeline/test-mathinfo.php?m=jnos-bolyai (705 words)

	[No title]
		Janos Bolyai was born in his grandparents’ home in Kolozsvar, Hungary (now Cluj, Romania) on December 15, 1802.
		Janos was the son on Farkas Bolyai and Zsuzsanna Benko.
		In 1891, the Janos Bolyai Mathematics Society was established, and in 1903 the Hungarian Academy of Sciences established the Bolyai Prize to be awarded every five years the mathematician whose work in the previous 25 years had given most to the progress of mathematics.
	www.southernct.edu /~pinciuv/mat530pr10.html (791 words)

	bolyai
		János Bolyai (1802-1860) was born in Koloszvar, now Cluj, a part of Transylvanian Romania, but in Bolyai's day a part of the Austro-Hungarian Hapsburg Empire.
		Apparently, Romania wants also to claim Bolyai for its own: There is a one-leu Romanian postage stamp bearing a picture of Bolyai, and there is the Babes-Bolyai University in Cluj-Napoca.
		Among the latter: Clairaut, Legendre, Beltrami, Farkas (Wolfgang) Bolyai, and a new (probably conjectured) image of his son, the eponymous János.
	www.siam.org /siamnews/12-04/bolyai.htm (1374 words)

	Bolyai János - Search Results - MSN Encarta (Site not responding. Last check: 2007-11-01)
		Bolyai, János (1802-1860), Hungarian mathematician, who was one of the founders of non-Euclidean geometry, independently of Nikolay Lobachevsky and...
		Bolyai, János (quotations): Mathematics: Out of nothing I have created a strange new…
		The mathematicians Carl Friedrich Gauss, Nikolay Lobachevsky, János Bolyai, and G. Riemann...
	uk.encarta.msn.com /Bolyai_J%C3%A1nos.html (104 words)

	Wallace-Bolyai-Gerwien Theorem
		According to Andreescu and Gelca, the property was proved independently by F. Bolyai (1833) and Gerwien (1835).
		(It should be mentioned that the Bolyai in question was a noted Hungarian mathematician Wolfgang Farkas Bolyai (1775-1856) and, sometimes Farkas Wolfgang Bolyai, father of Janos Bolyai, the co-inventor of the non-Euclidean geometry, and a dear friend of Johann Carl Friedrich Gauss.
		Like the birthplace of I. Kant, the birthplace of F. Bolyai has also changed hands.
	www.cut-the-knot.org /do_you_know/Bolyai.shtml (414 words)

	BOLYAI 200
		In 2002 we celebrate the bicentennial anniversary of the birth of János Bolyai, one of the creators of non-Euclidean geometry, by organizing an international conference in geometry and topology.
		Sections in history of mathematics will be dedicated to János Bolyai's life and scientific activity and its impact to the development of science.
		Abstracts for talks and posters should be submitted by email to the secretary of BOLYAI 200, bolyai@math.ubbcluj.ro.
	math.ubbcluj.ro /~bolyai/secann.htm (611 words)

	Bolyai - HighBeam Encyclopedia (Site not responding. Last check: 2007-11-01)
		The father, Farkas, or Wolfgang, Bolyai, 1775-1856, b.
		Bolya, Transylvania, was educated in Nagyszeben from 1781 to 1796 and studied in Germany during the next three years at Jena and Göttingen, where he began a lifelong friendship with Carl F. Gauss.
		Find newspaper and magazine articles plus images and maps related to "Bolyai" at HighBeam.
	www.encyclopedia.com /doc/1E1-bolyai.html (375 words)

	SIAM: Letters to the Editor: János Bolyai and Mathematical Bombshells
		Davis writes that Transylvania, the birthplace of the Bolyais, has been oscillating between Hungary and Romania for ages.
		Not so: Romania as a state was created by the Treaty of Versailles in 1919; Transylvania had been part of Hungary for a thousand years, except for a period in the 16th and 17th centuries, when Hungary was under Turkish occupation and Transylvania became an independent principality.
		Bolyai had studied the arithmetic of Gaussian integers, and used them to give an elegant proof that primes of form 4n + 1 can be written as a sum of two squares.
	www.siam.org /news/news.php?id=16 (315 words)

	Farkas (Wolfgang) Bolyai (Site not responding. Last check: 2007-11-01)
		Farkas Bolyai (Wolfgang in German) is remembered today primarily as a friend and lifelong correspondent of Gauss and as the father of János Bolyai, one of the discoverers of non-Euclidean geometry.
		Farkas was born in the Transylvanina region of Hungary (now part of Romania) and educated in Evangelical Reformed schools in Hungary until studying at the University of Göttingen from 1796 to 1799.
		This may not have been done, but in addition to two stamps in his honor, he and János have been remembered with the names of three Budapest streets.
	www.math.wfu.edu /~kuz/Stamps/FBolyai/BolyaiFarkas.html (244 words)

	Wolfgang Bolyai
		P Stäckel, W und J Bolyai, Geometrische Untersuchungen (Leipzig, 1913).
		L Dávid, In memoriam Wolfgang Bolyai (Hungarian), Magyar Tud.
		J Fráter, The library of Farkas Bolyai (Hungarian), Magyar Tud.
	www.shsu.edu /~icc_cmf/bio/bolyai.html (276 words)

	UNIVERSITATEA "BABES-BOLYAI" OF CLUJ-NAPOCA - GREEK CATHOLIC THEOLOGY
		After the Second World War, in 1945, the "Bolyai Janos" University was founded in Cluj, having Hungarian as language of teaching.
		Pursuant to the programme adopted by the Movement for Democracy in December 1989, the University management committed themselves to thrust the communist repercussions away from the University organising and functioning system.
		Furthermore, the Charter of the "Babes- Bolyai" University issued in 1992 stipulated that the University should join the major tradition of free thinking and democratic approaches to existence issues.
	www.ceebd.co.uk /ceeed/un/rom/ro019008.htm (2042 words)

	Read This: János Bolyai, Non-Euclidean Geometry, and the Nature of Space
		János Bolyai’s treatment of non-Euclidean geometry burst upon the mathematical scene in 1832 as an appendix (in Latin), entitled The Science Absolute of Space, to an elementary mathematical work of his father Farkas. Its impact, like that of the contemporaneous treatment of the subject by Nikolai Ivanovich Lobachevsky, was essentially nil.
		Yet today, we recognize Bolyai as being the co-creator of the subject of non-Euclidean geometry, a subject whose philosophical impact in the last decades of the nineteenth century was enormous and whose mathematical impact since the time of Einstein’s discovery of general relativity has also been significant.
		Publication Data: János Bolyai, Non-Euclidean Geometry, and the Nature of Space, by Jeremy J.
	www.maa.org /reviews/GrayBolyai.html (239 words)

	American Hungarian Foundation Janos Bolyai Lecture Series on Arts and Sciences (Site not responding. Last check: 2007-11-01)
		The Lecture Series honors Janos Bolyai, the world-renowned Hungarian mathematician born in 1802.
		October 18, 2002, Gyuri Hollosy, Sculptor and Professor: The Memorial Remembrance of the 1956 Hungarian Revolution in a Sculpture.
		Saturday, February 7, 2004 9:30AM-5:00PM the Bolyai Lecture Series on Arts and Sciences of the American Hungarian Foundation will organize a Symposium on John von Neumann’s life and work to commemorate the 100th anniversary of his birth.
	www.ahfoundation.org /bolyai (939 words)

	Shelah receives Bolyai prize (Site not responding. Last check: 2007-11-01)
		Saharon Shelah (Hebrew University, Jerusalem, Israel and Rutgers University, New Jersey) has been awarded the János Bolyai International Mathematical Prize of the Hungarian Academy of Sciences, which consists of a medal and an award of $25,000.
		This award was established in 1903 by the Hungarian Academy of Sciences in honor of János Bolyai, co-discoverer of non-Euclidean geometry, and was presented to H. Poincaré in 1905 and to D. Hilbert in 1910, after which various historical events, beginning with the first World War, forced its interruption.
		He also solved a number of famous problems arising in other branches of mathematics, such as algebra, combinatorics, and topology.
	www.math.rutgers.edu /docs/shelah.html (264 words)

	History of Mathematics [encyclopedia] (Site not responding. Last check: 2007-11-01)
		Mathematical activity in France (Gaspard Monge, Pierre Simon Laplace, Augustin Louis Cauchy), and subsequently in Germany (Carl Gauss, Carl Jacobi, Peter Dirichlet, Bernhard Riemann) was strongly developed and professionalized, in both research and teaching directions.
		The works of Niels Hendrik and Evariste Galois, two remarkable talents who died young, proved influential on later generations, as did the non-Euclidean geometry of Jçnos Bolyai and Nicolai Lobachevsky.
		The growing importance of numerical data in society led to the development of statistical thinking, notably in the work of Adolphe Quételet (1796--1874), with applications in both the physical sciences (eg James Clerk Maxwell) and biological and human sciences (eg Karl Pearson).
	www.kosmoi.com /Science/Mathematics/History (2656 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Janos Bolyai was born in Hungary and received his early education in mathematics from his mathematician father
		His father had hopes that he would go to Gottingen and study with Gauss, but Janos received a military education at the imperial engineering academy in Vienna.
		This demoralized Janos so much that, while he continued to work on mathematical problems, he published no more.
	www.math.wfu.edu /~kuz/Stamps/JanosBolyai/JBolyai.html (221 words)

	UNIVERSITATEA "BABES-BOLYAI" OF CLUJ-NAPOCA (Site not responding. Last check: 2007-11-01)
		After the war ended the University moved back to Cluj and started to operate in 1948 under the name of "Victor Babe\".
		In 1945, during the same communist period of Stalinist background, another university, this time a Hungarian one, was established and named after the mathematician Bolyai Janos.
		In 1959 the two institutions of higher education merged under the name University Babes-Bolyai in which teaching and research -in Romanian and Hungarian alike - were hampered by the communist regime of that time.
	www.euroeducation.net /un/rom/ro019020.htm (4846 words)

	Tuesday, October 1st, 2002
		Departure to Bolyai’s Memorial House (departure from1, Mihail Kogălniceanu street)
		Elective Course for the 9th Form (1 hour/week).
		– Homage to Bolyai János at his anniversary
	math.ubbcluj.ro /~bolyai/program.html (413 words)

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