
	Where results make sense

Topic: Bolyai, Janos

Related Topics

Carl Gustav Jacobi

Elliptic geometry

Carl Friedrich Gauss

Hyperbolic geometry

Caransebes

Felix Klein

Timisoara

Transylvania

Banat

Dacia

Schwaben

Body piercing

Sinaia

List of Lunar craters

List of mathematicians

In the News (Fri 1 Jan 10)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	János Bolyai - Wikipedia, the free encyclopedia
		János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician.
		Bolyai's work was published in 1832 as an appendix to an essay by his father.
		In 1848 Bolyai discovered not only that Lobachevsky had published a similar piece of work in 1829, but also a generalisation of this theory.
	en.wikipedia.org /wiki/J%C3%A1nos_Bolyai (271 words)

	KISS ELEMER A Bolyai ladak legujabb titkai
		Milyen forrásból értesült a geométerként ismert Bolyai János az algebra egyik alapvetõ problémájáról?
		Valószínû, hogy Bolyai János érdeklõdését a feladat iránt éppen Gauss említett mûvei és Ettingshausen könyve keltették fel.
		Érdekes, hogy Bolyai János is érezte: az algebra alaptételét tisztán algebrai módszerekkel kellene bebizonyítani.
	www.kfki.hu /~tudtor/tallozo1/kisse3.html (2171 words)

	Bolyai (Site not responding. Last check: 2007-11-06)
		Bolyai was posted to Arad in 1826 and there he found that Captain Wolther von Eckwehr, one of his old teachers of mathematics from the Academy in Vienna, was also stationed.
		Bolyai gave him a draft of the materials which he was writing on the theory of geometry, probably because he hoped for some constructive comments from him.
		It seems that Farkas Bolyai did not approve of Rozália, was unhappy about his son's financial position, was unhappy that the family estate at Domáld was not being properly cared for, and was unhappy that his son was damaging his good name for Farkas was a highly respected member of the community.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Bolyai.html (2309 words)

	KöMaL: Angol szám, 2002. december
		Bolyai's discovery is not only the first step in the development of modern mathematics, but his ideas had a significant impact on the shaping of natural sciences in general.
		His father, Farkas Bolyai (1775-1856), became later the erudite professor of the college of Marosvásárhely, whereas his mother, Zsuzsanna Benkő (1782-1821) was the daughter of a surgeon from Kolozsvár.
		János Bolyai preserves all Euclides's postulates except Postulate V. Just as in common perception, all those basic assumptions which underlie the connecting of points with the help of lines and planes, the transfer of distances and angles with the same extent or the congruence of triangles etc. are also requirements of the S-system.
	www.komal.hu /lap/2002-ang/bolyai.h.shtml (3269 words)

	JANOS BOLYAI (1802-1860) (Site not responding. Last check: 2007-11-06)
		Janos Bolyai was born on December 15, 1802 in Kolozsvar, Austrian Empire, which is now Cluj, Romania.
		Janos studied at the Royal Engineering College in Vienna from 1818-1822.
		Janos died on January 27, 1860 in Marosvasarhely, Autrian Empire, which today is Tirgu-Mures, Romania.
	www.southernct.edu /~pinciuv/mat360pr10.html (281 words)

	New Page 13 (Site not responding. Last check: 2007-11-06)
		His father, Farkas Bolyai was a teacher of the Lutheran Catholic College in Targu Mures as well as a corresponding member of the Hungarian Academy of Sciences.
		Janos Bolyai at the age of 12 accomplished the fourth form of secondary school.
		Knowing the fact that Janos Bolyai had difficult financial circumstances and did not have optimal conditions to a creative professional work, his scientific results shall be acknowledged and respected even more.
	www.uni-miskolc.hu /koliweb/koli2eng/index2.htm (663 words)

	Abstracts (Site not responding. Last check: 2007-11-06)
		Ezek közül minden bizonnyal a legérdekesebb az, amely azt bizonyítja, hogy Bolyai János fiatal korában nem csak a szögharmadolással, de a kockakettõzés feladatával is foglalkozott.
		Látható, hogy Bolyai János itt is a lehetõ legáltalánosabban mondta ki a feladatot.
		Bolyai's non-Euclidean way of thinking is reflected in his opinions concerning the intrinsic relation that exists between the physical gravity and geometric space: ".the law of gravity shows a strong connection with the nature of space, with the existence (structure) and variety of void".
	www.uni-miskolc.hu /hmtm/abstracts.html (4577 words)

	On Gauss' Mountains (Site not responding. Last check: 2007-11-06)
		The other person credited with discovering non-Euclidean geometry, Janos Bolyai, was the son of Wolfgang Bolyai, who was a friend (almost the only friend) of Gauss during their school days at Gottingen in the late 1790's.
		Janos found (as had Gauss, Taurinnus, and Lobachevesky just a few years earlier) that Euclid's parallel postulate is not a consequence of the other postulates, but is rather an independent assumption, and that alternative but equally consistent geometries based on different assumptions may be constructed.
		Janos Bolyai was so embittered by Gauss's backhanded response to his non-Euclidean geometry that he never published again.
	www.mathpages.com /rr/s8-06/8-06.htm (1554 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_Farkas (Site not responding. Last check: 2007-11-06)
		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.
		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.
		Bolyai taught his son János mathematics, for this was the subject which he hoped that he would follow.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Bolyai_Farkas.html (1679 words)

	Janos Bolyai Article, JanosBolyai Information (Site not responding. Last check: 2007-11-06)
		János Bolyai (December 15, 1802 – January 27, 1860)was a Hungarian mathematician.
		Gauss, on reading the Appendix, wrote to a friend saying"I regard this young geometer Bolyai as a genius of the first order".
		In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers.Although he never published more than the 24 pages of the Appendix, he left more than 20000 pages of manuscript of mathematicalwork when he died.
	www.anoca.org /he/work/janos_bolyai.html (281 words)

	Bolyai, János (Site not responding. Last check: 2007-11-06)
		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)

	Lecture 15 (Site not responding. Last check: 2007-11-06)
		Farkas Bolyai (1775-1856) became interested in the foundations of geometry and the parallel axiom while studing at the university, where he was a closed freind of Gauss.
		Son of Farkas Bolyai, Janos Bolyai (1802-1860), followed the path of his father and began his own investigations on the parallel postulate.
		Janos published the results of his research in 1831 as an appendix to the Tentamen, written by his father.
	www.math.ntnu.no /~eugenia/MA2401/lec15.html (304 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Janos Bolyai was born in Hungary and received his early education in mathematics from his mathematician father
		He entered the military and served until he was pensioned off for ill health; he returned to his hometown of Marosvasarhely where he lived for the rest of his life.
		His father was a college friend of the now famous Gauss, but when Farkas sent Janos' work to Gauss, Gauss replied that it was fine work, but he could not praise it, for this would be self-praise, since he had developed a similar theory years before.
	www.mthcsc.wfu.edu /~kuz/Stamps/JanosBolyai/JBolyai.html (221 words)

	THE 200 YEARS OF BOLYAI, CONSTRUER OF NONEUCLIDEAN GEOMETRY
		In citations of form [@X] the material is an unpublished packet of numbering X of the Bolyai manuscripts in the Teleki Téka, and K x/y is a numbered Bolyai manuscript in the Manuscriptorium of the Hungarian Academy of Sciences, Budapest.
		Bolyai János has shown that the Euclidean axiom of parallels can be substituted with another, and the construction remains OK. So as a mathematical possibility/virtuality it exists.
		Bolyai lives at the farm of his father, on Domáld/Viisoara, with his 2 small children Dénes (1837) and Amália (1840) and the housekeeper kibédi Orbán Róza of Kóródszentmárton (Sedes Maros).
	www.rmki.kfki.hu /~lukacs/BOLYAI.htm (13891 words)

	Bolyai, János (Site not responding. Last check: 2007-11-06)
		Although Bolyai knew nothing of mathematics at the age of 10, by the age of 13 he had mastered calculus and analytic mechanics under the tutelage of his father, the distinguished mathematician Farkas Bolyai.
		This was a profound blow to Bolyai, even though Gauss had no claim to priority since he had never felt enough confidence in his findings to publish them.
		Bolyai allowed the "Appendix" to be published with his father's Tentamen Juventutem Studiosam in Elementa Matheseos Purae Introducendi (1832; "An Attempt to Introduce Studious Youth to the Elements of Pure Mathematics"), but the essay went unnoticed by other mathematicians.
	www.phy.bg.ac.yu /web_projects/giants/bolyai.html (401 words)

	Search Results for bolyai (Site not responding. Last check: 2007-11-06)
		Bolyai taught his son Janos mathematics, for this was the subject which he hoped that he would follow.
		Bolyai did not remain long in Lemberg for in 1832 he was posted to Olmutz where he was now a captain.
		It seems that Farkas Bolyai did not approve of Rozalia, was unhappy about his son's financial position, was unhappy that the family estate at Domald was not being properly cared for, and was unhappy that his son was damaging his good name for Farkas was a highly respected member of the community.
	www-history.mcs.st-and.ac.uk /history/Search/historysearch.cgi?BIOGINDEX=bolyai (1898 words)

	Janos Bolyai, Euclid, and the Nature of Space - The MIT Press (Site not responding. Last check: 2007-11-06)
		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)

	References for Bolyai (Site not responding. Last check: 2007-11-06)
		A C Albu, János Bolyai and the foundations of geometry (Romanian), in Proceedings of Symposium in Geometry (Cluj-Napoca, 1993), 7-23.
		E Sarlóska, János Bolyai, the soldier (Hungarian), Magyar tudományos akadémia matematikai 15 (1965), 341-387.
		T Toro, János Bolyai and the geometrization of the fundamental physical forces of nature (Romanian), in Proceedings of the János Bolyai Symposium (Cluj-Napoca, 1979), 112-125.
	www-gap.dcs.st-and.ac.uk /~history/References/Bolyai.html (289 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.
		The story of the simultaneous discovery (or the creation) of non-Euclidean geometry by Bolyai and Lobachevsky, and of its consequences, has been told many times over and at different levels of mathematical sophistication and purpose.
	www.siam.org /siamnews/12-04/bolyai.htm (1374 words)

	The Hutchinson Dictionary of Scientific Biography: Bolyai, Farkas Wolfgang (1775-1856 and Bolyai, Janos 1802-1860)@ ... (Site not responding. Last check: 2007-11-06)
		The Hutchinson Dictionary of Scientific Biography: Bolyai, Farkas Wolfgang (1775-1856 and Bolyai, Janos 1802-1860)@ HighBeam Research
		Wolfgang Bolyai was born at Nagyszeben, in Hungary (now Sibiu, Romania), on 9 February 1775.
		For the rest of his life the elder Bolyai was a professional mathematician, teaching at the Evangelical Reformed College at Nagyszeben and then at the college at...
	www.highbeam.com /library/doc0.asp?DOCID=1P1:28910566&refid=ip_encyclopedia_hf (192 words)

	Wolfgang Bolyai
		Farkas Bolyai was the father of János Bolyai and studied at Jena, then at Göttingen where he was taught by Kaestner.
		Farkas Bolyai was interested in the foundations of geometry and the parallel axiom.
		Farkas Bolyai wrote to his son Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.
	www.shsu.edu /~icc_cmf/bio/bolyai.html (276 words)

	Science - Janos Bolyai (Site not responding. Last check: 2007-11-06)
		Written in Latin, it was meant as a complementary work to his father's, Bolyai Farkas, manual titled: "Tentamen".
		In 1837 Bolyai also dedicated his study "Responsio" to complex numbers theory.
		His findings are dialectical contributions to mathematical problems, as he laid new foundations to geometry and prepared it for new horizons.
	www.ici.ro /romania/en/stiinta/bolyai.html (117 words)

	The Hyperbolic Axiom and its Consequences
		It is often called Bolyai-Lobachevskiian geometry after two of its discovers János Bolyai and Nikolai Ivanovich Lobachevsky .
		Bolyai first announced his discoveries in a 26 page appendix to a book by his father, the Tentamen, in 1831.
		Another of the great mathematicians who seems to have preceeded Bolyai in his work is Carl Fredrich Gauss .
	www.math.uncc.edu /~droyster/math3181/notes/hyprgeom/node44.html (381 words)

	JÁNOS BOLYAI CONFERENCE ON HYPERBOLIC GEOMETRY
		János Bolyai (15 December 1802-27 January 1860) was born in Kolozsvár, Transylvania, at that time a Hungarian Grand Duchy ruled by the Hapsburgs, and died in Marosvásárhely, Transylvania.
		After he had recognized the impossibility of this task, he developed absolute geometry that is independent of the fifth postulate and also hyperbolic geometry where this postulate is negated.
		In 2002 we celebrate the bicentennial anniversary of the birth of János Bolyai, the genius geometer, one of the creators of hyperbolic geometry.
	www.conferences.hu /Bolyai (1465 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)

	2nd EUROPEAN CONGRESS OF MATHEMATICS
		János Bolyai Mathematical Society is pleased to invite you to attend the Second European Congress of Mathematics, to be held under the auspices of the European Mathematical Society in Budapest, Hungary, July 21-27, 1996.
		Situated on both sides of the river Danube, Budapest is one of the great metropolises of Europe, endowed with a unique combination of natural and architectural beauty: charming hills, graceful bridges, a royal palace, elegant boulevards, pleasant parks, cafés, concert halls, art collections, and more, all this linked by efficient public transportation.
		Bolyai Society invites you to combine a week of mathematical adventure and a few days of unforgettable vacation in our ``little Paris on the Danube'', as the National Geographic called our city.
	www.emis.de /ECM2/first-announcement.html (715 words)

	János Bolyai, Non-Euclidean Geometry, an... - Wikipedia, the free encyclopedia
		We don't have an article called "János Bolyai, Non-Euclidean Geometry, an..."
		Search for "János Bolyai, Non-Euclidean Geometry, an..." in...
		Wait a few minutes, or check the deletion log.
	en.wikipedia.org /wiki/J%C3%A1nos_Bolyai,_Non-Euclidean_Geometry,_an... (39 words)

	Farkas (Wolfgang) Bolyai (Site not responding. Last check: 2007-11-06)
		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.mthcsc.wfu.edu /~kuz/Stamps/FBolyai/BolyaiFarkas.html (244 words)

	KöMaL: English issue, December 2002
		János Bolyai's inquiries concerning Fermat's two-square theorem are very valuable.
		Bolyai did not know about either Abel's or his contemporary's, Evariste Galois's (1811-1832) works.
		Above all, János Bolyai would have deserved much better recognition.
	www.komal.hu /lap/2002-ang/bolyai.e.shtml (3269 words)

Try your search on: Qwika (all wikis)