61. History nikolai lobachevsky (17921856) was a Russian mathematician, and the firstto publish a complete book about this imaginary geometry in 1829. http://www.math.youngzones.org/Non-Egeometry/history.html

Proving a Postulate Girolamo Saccheri (1667-1733) was a Jesuit priest from Italy. First to try proving the parallel postulate using a proof by contradiction, h e uncovered two new types of geometry. Carl Friedrich Gauss (1777-1855) was a German mathematician who tried to prove the fifth postulate. He assumed that multiple parallel lines existed and thought that other types of geometry might exist. He developed hyperbolic geometry, but never went public for fear of controversy. Janos Bolyai (1802-1860) was a Hungarian Army officer and a mathematician. He assumed that there were more than one parallel line and published his findings in 1832. He wrote, "out of nothing I have created a strange new world." Nikolai Lobachevsky (1792-1856) was a Russian mathematician, and the first to publish a complete book about this "imaginary geometry" in 1829. This year is considered the birth of Non-Euclidean geometry. Bernhard Riemann (1826-1866) was a German mathematician. He wrote his doctoral dissertation under the supervision of Gauss. His inaugural lecture in 1854 reconfigured the entire concept of geometry. His work was in spherical geometry.

62. L Index 234) Listing, Johann (124*) Littlewood, Dudley (506*) Littlewood, John E (298*)Livsic, Moshe (626*) Llull, Ramon (348) lobachevsky, nikolai (2143*) Löwner http://www.math.hcmuns.edu.vn/~algebra/history/history/Indexes/L.html

63. Science In Pre-revolutionary Russia Kagan, N. lobachevsky and His Contribution to Science (Moscow Foreign LanguagesPublishing House, 1957 Kosmodemyansky, AA nikolai Zhukovsky (Moscow Mir, 1987 http://web.mit.edu/slava/guide/Biblio/3.htm

Virtual Guide to the History of Russian Science and Technology Archives Bibliography Institutions ... Contact Science in Pre-Revolutionary Russia General Mathematics Astronomy Physics ... Back to Main Catalogue To add an entry or an annotation to this Bibliography , send e-mail to slava@mit.edu Science in Pre-Revolutionary Russia: General Sources in English: Denny, Joseph H., and Paul M. Mitchell. "Russian Translations of the ," in Frank A. Kafker, ed., (Oxford: The Voltaire Foundation, 1994). Graham, Loren R. Science in Russia and the Soviet Union: A Short History (Cambridge, Mass.: Cambridge University Press, 1993). Griffith, D. "The Early Years of the Petersburg Academy of Sciences as Reflected in Recent Soviet Literature," Canadian-American Slavic Studies Lipski, Alexander. "The Foundation of the Russian Academy of Science," Isis Ryan, W.F. "Scientific Instruments in Russia from the Middle Ages to Peter the Great," Annals of Science Schulze, Ludmilla. "The Russification of the St. Petersburg Academy of Sciences and Arts in the Eighteenth Century," British Journal of the History of Science Sevcenko, Ihor. "Remarks on the Diffusion of Byzantine Scientific and Pseudo-Scientific Literature among the Orthodox Slavs,"

64. Bruch Und Reparatur - Wohnen An Der Front Des Denkens Translate this page 1829, in dem Jahr, als nikolai Ivanovich lobachevsky seine Theorie einer nicht-euklidischenGeometrie veröffentlichte, war die einst enge Verbindung zwischen http://www.heise.de/tp/deutsch/special/arch/6068/5.html

Bruch und Reparatur - Wohnen an der Front des Denkens 1829, in dem Jahr, als Nikolai Ivanovich Lobachevsky seine Theorie einer nicht-euklidischen Geometrie veröffentlichte, war die einst enge Verbindung zwischen Architektur und dem Rand des Wissens bereits nahezu aufgelöst. Fast gleichzeitig veröffentlichte Victor Hugo 1830 "Notre Dame de Paris", eine Erzählung, die ein architektonisches Werk in Buchform ist. 1832 gab Hugo die zweite und endgültige Fassung von "Notre Dame de Paris" heraus, der er ein Kapitel mit der Überschrift "Ceci Tuera Cela" (Dies wird jenes töten) hinzugefügt hatte. Das ganze Buch, besonders aber dieses Kapitel, setzt sich ausführlich mit der Erkenntnis auseinander, daß das Buch die Architektur getötet hat. Platon erwartete nicht, daß das menschliche Wissen statisch sein würde, auch wenn er sich vorstellte, daß die ideale Welt dies wäre. Zu Beginn des Timaios macht er deutlich, daß die im Folgenden ausgeführte Theorie nur eine "wahrscheinliche Erzählung" sei. Sie sei zwar so gut, wie man sie zu hören erwartet, aber bleibe nichtsdestoweniger eine Erzählung, weil Menschen niemals die Wirklichkeit vollständig erkennen können. Diese Annahme impliziert, daß dann, wenn sich das menschliche Wissen verändert, so bruchstückhaft und fehlerhaft es auch sein mag, auch die damit zusammenhängende Architektur sich verändern müsse: eine langsame Kunst, die dem langsamen Wachstum der menschlichen Erkenntnis folgt.

65. Noiseloop.com our days nikolai Ivanovich lobachevsky Who made me the geniusI am today, The mathematician that others all quote? Who's the http://www.noiseloop.com/article.php?sid=35

66. InTune || Tom Lehrer, Part II lobachevsky Ah. The gem in this CD. This is possibly the funniest song on thisCD, about the grrreat mattematishun nikolai Ivanovich lobachevsky. Oy! http://www.intune.org/story/2001/3/2/95047/37595

Live Recordings Tools Diaries ... Home   Music discussion for the soul submit story create account faq mission ... search Tom Lehrer, part II Recordings By Sinfonos , Mon Mar 5th, 2001 at 08:51:57 PM EST Alright, so I borrowed another Tom Lehrer CD from a friend Tom Lehrer Revisited . So here's another non-classical review from me :-P For those of you who don't know Tom Lehrer... he's the most brilliant creative genius that America has produced in almost 200 years, endowed with the most glorious baritone voice to be heard on an American stage, endowed with twelve incredibly agile fingers, who had a long and varied career in the field of entertainment, with 9 years starting at Harvard University... (OK, that was a joke blatantly ripped off the first track of this CD, so sue me! :-P) Alright, so here are the tracks on this CD. These are the songs Lehrer plays in his concert. Personally, although some of the stuff here is pretty good, I still prefer the first CD, An Evening Wasted with Tom Lehrer . It could be because of the audience response... the audience in this CD obviously had heard most of the songs before, so there weren't enough laughs to make it funny. Introduction where Tom Lehrer introduces himself humbly in the third person. No songs on this track, but it's extremely funny.

67. The Radical Exponent 21.2 ridicule. Priority of publication goes to nikolai lobachevsky, who publishedhis results on nonEuclidean geometry in 1829 in Russian. A http://www.nwmissouri.edu/~math/radexp212.html

The Radical Exponent Volume XXI, Number 2, April 1997 Table of Contents When Parallels Diverge The Problem Corner The Problem Corner - Solutions to Previous Problems 1997 Mathematics Olympiad ... Summer 1997 Courses Publishing and correspondence information for The Radical Exponent When Parallels Diverge by Michael Motto In the Elements , Euclid derived all of geometry (and other areas of mathematics) from a set of just ten statements which he assumed to be true. These statements were in turn divided into two groups: the five common notions, which were applicable to all areas of mathematics, and the five postulates, which applied specifically to geometry. Unfortunately, while most of the common notions and postulates were simple, straightforward sentences, the fifth postulate, also known as the parallel postulate, looked a little worse: If a line segment falls on two other line segments in such a way that the interior angles on the same side are less than two right angles, then the two line segments, if extended indefinitely, meet on that side on which the angles are less than the two right angles. The unpleasant appearance of this statement is due in part to the fact that mathematicians of the past were less comfortable about dealing with infinity, so Euclid was trying to word things in terms of a finite figure. A simpler, equivalent statement was written by John Playfair in 1795 although it does require us to imagine the infinite extent of the lines described:

68. 1001 Russia Page - All-Entrances Lewitsky, Ilia Lifshits, Ivan Likhachev, Lipetsk, Boris Livanov, Nicolai lobachevsky,lobachevsky Geometry, Lokai (Horse's Breed), nikolai Logunov, Mikhail http://sungraph.jinr.dubna.su/valeri/all-ent.html

1001 Well-Known Words Associated with Russia ALL ENTRANCES Note: for convenience some "the" and other articles weren't included. Now # is in the table Words A-Z, Proverbs, Citations, Ideas A Abramtsevo, Abrauo-Byurso, Ales' Adamovich, Aeroflot , U2 Affair, "Golden Age", Ivan Aivazovsky, AK-74, Akhal-Teke , Anna Akhmatova, Akakiy Akakievish, Vasily Alekseev, Alexander Alyehin, Alexander I, Alexander III, Akademgorodok, Patriarch Alexii II, Svetlana Allilyueva, Alexander Alyabiev, Altai, AMO, Yuri Andropov, Angara, Anglo-Karabardin, Yuri Annenkov, Pyotr Anohin, "ANTEY", Pavel Antokol'sky, Anosov, Oleg Antonov (Aircrafts), Antonovka, Alexander Arakcheev, Arakcheevschina, Arbat, Irina Arkhipova, Inessa Armand, Red Army, Vladimir Arsen'ev, Victor Astaf'ev, Arkhangel'sk, "ARTEK", Ivan Artobolevsky, Port Artur, Issac Asimov, Astrakhan', Vladimir Atlantov, Atomizdat, Atommash, Avos', Avos'ka, "Avrora", Azbuka, B C Sour Cabbage, Isaakievskiy Cathedral, Kazanskiy Cathedral, Black Caviar, Red Caviar, Russian Blue Cat, Catherine II (The Great), CCCP, Novodevichii Cemetery, "Chaika", Alexander Chakovsky, Soviet Champagne, Pyotr Chaadaev, Vasiliy Chapaev, Chastushka, Chechnya, CheKa (OGPU, NKVD), Anton Chekhov, 1968 Year in Chekhoslovakiya, Semen Cheluskin, Chelyabinsk, Boris Cherkov, Konstantin Chernenko, Chernobyl , Nikolay Chernishevsky, Chita, "Ochi Chornyie", Chervonets, ~chev (Ending of Second name), Marshall Vasiliy Chyuikov, Kornei Chukovskii, Ortodox Church, Church of Basil the Beatified (Pokrovski Cathedral), Alexandra Collontay, Collectivization, Collkhoz, Comintern, Comissariat, Communizm, Communist, Communist's Blok, Committee of Ministers, Committee of Party's Control, Committee of Soviet Women, Commonwealth of Independent States (CIS), Podsdam Conference, Tegeran Conferenca, Yalta Conference, Congress of People's Deputies, 20th Congress of Communist Party, "Cosmos" (Hotel), Cosmodrom, Cosmonavt, People's Commissar, CPSU

69. The XVII Mendeleev Congress Great mathematician nikolai lobachevsky, known all over the world as the founderof nonEuclidean geometry, was the rector of Kazan University for 19 years. http://mendel.knc.ru/javaless/info.html

Information Introduction Venue Language Dates Organisation Programme Scientific programme Pre-conference tours Post-conference tours Conference Events Special Events Exhibition Registration Visas Registration fees Payments Abstracts Registration form Accommodation Contact Information Russian version INTRODUCTION The Mendeleev Congresses on General and Applied Chemistry are the most prestigious national forums of Russian chemists and traditionally take place every 5 years. The first Mendeleev Congress, held in St. Petersburg in 1907, was dedicated to the memory of the great Russian chemist D.I. Mendeleev. Subsequent Congresses were held in Moscow, Leningrad, Kazan, Kharkov, Kiev, Alma-Ata, Baku, Tashkent and Minsk. The last XVI Mendeleev Congress under the title "Chemistry on the Threshold of XXI Century" took place in St. Petersburg in 1998. The Congress was timed to coincide with the 250th anniversary of the first chemical laboratory in Russia, founded and headed by the world-renowned Russian scientist and scholar M.V.Lomonosov.

70. The Hyperbolic Axiom And Its Consequences geometries. It is often called BolyaiLobachevskiian geometry after twoof its discovers János Bolyai and nikolai Ivanovich lobachevsky . http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node44.html

Next: Angle Sums (again) Up: Hyperbolic Geometry Previous: Hyperbolic Geometry The Hyperbolic Axiom and its Consequences What is hyperbolic geometry ? It is an example of one of many non-euclidean geometries. It is often called Bolyai-Lobachevskiian geometry after two of its discovers and Nikolai Ivanovich Lobachevsky . Bolyai first announced his discoveries in a 26 page appendix to a book by his father, the Tentamen , in . You can read about what happened to him and his work in the text. Another of the great mathematicians who seems to have preceeded Bolyai in his work is Carl Fredrich Gauss . He seems to have done some work in the area dating from 1792, but never published it. The first to publish a complete account of non-euclidean geometry was Lobachevsky in . It was first published in Russian and was not widely read. In he published a treatise in German. We shall add one more axiom to the list of axioms for Neutral Geometry. HYPERBOLIC AXIOM In hyperbolic geometry there exists a line and a point P not on such that at least two distinct lines parallel to pass through P We shall denote the set of all points in the plane by , and call this the hyperbolic plane Lemma 12.1:

71. Contents, Volume 2 Analysis of the logical work of the Russian philosopher nikolai Aleksandrovich Vasil logicsagainst the influence of his studies of lobachevsky's noneuclidean http://www.ed.ac.uk/philosophy/ml/abs2.html

Modern Logic Contents and abstracts for Modern Logic Volume 2 Vol. 2, no. 1 Vol. 2, no. 2 Vol. 2, no. 3 Vol. 2, no. 4 Modern Logic /1, September 1991 Irving H. ANELLIS Editor's Note: Burgin and the theory of named sets Modern Logic Brief discussion of the origin of Burgin's and Kuznetsov's work on the theory of named sets. The structure and development of mathematical theories Modern Logic The authors present a description of the theory of named sets and give an application of the theory to a category-theoretic analysis of the structure and development of mathematical theories. Thomas DRUCKER Discussion. History and grammar Modern Logic A brief summary and critical assessment of Colin McLarty's treatment of the history of topos theory. Jacqueline BRUNNING C.S. Peirce's relative product Modern Logic Examines a historical and mathematical connection between C.S. Peirce's algebra of relations and Benjamin Peirce's linear associative algebra, showing that the central operation in the algebra of relatives of relative product was borrowed from the multiplicative operation of linear associative algebra. Fania CAVALIERE Review-essay of N.A. Vasil`ev

72. Korobova Galina Russia Moscow Region, Dubna, Joint Institute For Kupriyanov nikolai Russia Moscow, Central Collector of Libraries, Department Head. KastosovIgor Russia Nizhni Novgorod, NI lobachevsky State University Museum http://www.gpntb.ru/win/inter-events/crimea2002/eng/user.cfm?qvr=K

73. The Village Voice Theater Not-Right Triangles By Michael t least according to the Tom Lehrer song about him, nikolai Ivanovich lobachevsky,inventor of nonEuclidean geometry, sold his theorems to MGM, which turned http://www.villagevoice.com/issues/0015/feingold.php

74. The Pride Of Russian Culture Notable library users at this time included the future Decembrist Wilhelm Kiichelbecker,the mathematician nikolai lobachevsky and the explorer Fiodor Litke. http://www.nlr.ru/eng/nlr/history/index4.html

Modest Korff. Engraving by Ivan Pozhalostin. 1877 Ivan Delianov. Lithograph by Peter Borel from a photograph by Steinberg. 1860s T The opening of the Public Library which coincided with what Pushkin called the time of "glory and delight" was recorded in all the St Petersburg newspapers. The poet and critic Piotr Pletnev wrote that all men and women whose "Russian hearts beat stronger on hearing the word Motherland" had perceived the event as "a glorious occurrence" important for the future of the country. The library remained a popular topic in subsequent years too. The papers described it as "a tmly national repository" and noted that any reader "had free entry to it, whatever title or rank he may have held." The Olenin years, in the course of which over 15,000 library cards were issued and some 100,000 volumes given out to readers, also saw the first attempts to analyse reading patterns, the range of subjects which interested users of the library and the demand for works by particular authors (Lomonosov, Karamzin, Derzhavin, Krylov, Zhukovsky, Gnedich, Batiushkov, and others). The same period was marked too by the inception of a reference and bibliographical service within the library as members of staff began to select literature systematically in response to readers' requests (books, for example, on the history of the 1812 War, Suvorov's campaigns in Italy and Switzerland, or public education in Russia). At the request of Stroganov and Olenin, the book-dealer Vastly Sopikov, a member of the merchant class, was taken into state service at the library. Sopikov had become famous for his knowledge in the field of Russian bibliography and the book trade. He was entmsted with managing the Russian stocks and the library saw to the publication of his major work An Essay in Russian Bibliography which the author per-spicaciously believed "will be a classic not only in Russia but also in foreign parts". Sopikov's work contained "an accurate and thorough description" of books published in Russia from the introduction of printing to the beginning of the nineteenth century and still remains a valuable handbook for librarians and bibliographers today.

75. Bigchalk: World Book Online geometry is sometimes called Lobachevskian geometry, because it was developedinthe early 1800'sby the Russian mathematician nikolai lobachevsky. http://worldbook.bigchalk.com/221160.htm

Geometry Geometry, jee AHM uh tree, is a branch of mathematics. Geometry involves studying the shape, size, and position of geometric figures. These figures include plane (flat) figures, such as circles, triangles, and rectangles, and solid (three-dimensional) figures, such as cubes, cones, and spheres. The name geometry comes from two Greek words meaning earth and to measure. The earliest uses of geometry included measuring lengths and areas of land. Most scholars believe that the ancient Egyptians were the first people to make extensive use of geometry. Geometry is important for many reasons. The world is full of geometric shapes. For example, snowflakes are shaped like hexagons (six-sided figures), and earthworms are shaped like cylinders. Houses and buildings have rectangular walls, and many bridges have triangular supports. Because geometric shapes are all around us, we can better understand and appreciate our world by knowing something about geometry. Geometry also has practical applications in many fields. For example, architects and carpenters must understand the properties of geometric objects to construct stable and attractive buildings. Navigators of airplanes, ships, and spacecraft rely on geometric ideas to chart and follow the correct course. Designers, engineers, metalworkers, and photographers also use geometric principles in their jobs. Geometry as a logical system Deductive reasoning is important in the study of geometry. Deductive reasoning begins with statements that are already accepted as true. These truths are then combined in a logical way to reach a conclusion. When the original statements are true, correct deductive reasoning always leads to true conclusions.

76. Russia & NIS - Cultural Values The mathematician nikolai lobachevsky (neeko-LI loh-bah-CHEF-skee, 1793-1856),chemist Dmitrii Mendeleev (DMEE-tri men-DEHLE-ehf, 1834-1907), electricity http://wrc.lingnet.org/rniscult.htm

Area Studies / Russian and the NIS Cultural Values Russian and American Cultural Values Values Expressed Through Proverbs Russian Soul Education ... Further Study Russian and American Cultural Values Area Map Cultural Values Acknowledgements In his book, From Nyet to DaUnderstanding the Russians , Yale Richmond discusses similarities and differences between American and Russian cultural values. Mr. Richmond bases his findings on over thirty years of day-to-day contact with the peoples of Russia and the Newly Independent States. While on assignments with the Department of State, U.S. Information Agency, Commission on Security and Cooperation in Europe and the National Endowment for Democracy, Yale Richmond oversaw cultural, education and science exchanges with the peoples of this region. Similarities. Continent orientation. Both the United States and Russia are great world powers, comprised of many ethnic groups, and inhabiting vast amounts of land area. Frontier spirit.

77. Chris' Bookmarks - Mathematics Golden Rectangle Golden Ratio; Greg and Colin's Golden Ratio Extravaganza;The Golden Ratio; The Law of Large Numbers; nikolai Ivanovich lobachevsky. Back. http://www.inhouse.com.au/links/maths.html

Mathematics The Golden Section - the Number and Its Geometry Fibonacci Numbers and the Golden Section Greg and Colin's Golden Ratio Extravaganza The Golden Ratio ... Back

78. Untitled Education. nikolai lobachevsky Anton Chekhov A) Elementary. Pavel ChebyshevMaxim Gorky B) Secondary. Sophia Kovalevskaia Alexander Blok C) Higher. http://www.shsu.edu/~his_ncp/366Outp.html

HISTORY 366: RUSSIAN HISTORY SINCE 1917. LECTURE OUTLINES. Lecture 7: THE GOLDEN AND SILVER AGES OF RUSSIAN CULTURE. TERMS: Avant-Garde Symbolists OUTLINE: I. Development of Russian Culture to 1860. gymnasia Leon Tolstoy II. Education. Nikolai Lobachevsky Anton Chekhov A) Elementary. Pavel Chebyshev Maxim Gorky B) Secondary. Sophia Kovalevskaia Alexander Blok C) Higher. Dmitrii Mendeleyev Andrei Belyi III. Science Alexander Kovalevskii Michael Glinka IV. Societies and Publications. Ivan Sechinov Modest Mussorsky VI. Art. Fyodor Dostoyevskii Michael Borodin VII. Music. Ivan Turgenev Nikolai Rimskii-Korsakov VIII. Conclusions Symbolists Petr Tschaikovsky Lecture 13: THE FEBRUARY AND OCTOBER REVOLUTIONS. Part 1: Toward the February Revolution. I. Deteriorating War Effort. a) Casualties. b) Stalemate and Defeat. c) Restiveness in the Armed Forces. II. Scandal and Political Instability. a) The Tsar and His Family. b) The Ministries. c) The Duma. III. Economic and Social Distress. a) War's Affect on the Economy. b) Unrest in Town and Country. IV. The February Revolution. a) The Closing of the Duma. b) The Food Riots and the Military. c) The Abdication and the Formation of the Provisional Government. V. Conclusions.

79. User Talk:Looxix - Wikipedia Hello and Welcome! I hope you like the place. mav. Hi, Looxix. Nice work on NikolaiIvanovich lobachevsky. This article was wainting for someone to start it. http://www.wikipedia.org/wiki/User_talk:Looxix

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help User talk:Looxix From Wikipedia, the free encyclopedia. Hello and Welcome! I hope you like the place. mav Hi, Looxix. Nice work on Nikolai Ivanovich Lobachevsky . This article was wainting for someone to start it. I'll try to tide up a bit more your quite huge stub - when I find a time. Shall we use naming of Lobachevsky instead of Lobachevskii in it? Check out also other great Russian mathematicians (e.g. Pafnuty Lvovich Chebyshev and his most talented student Aleksandr Mikhailovich Lyapunov ...) Best regards. XJamRastafire Hi there. I see you've just created Gravitational lense however there's already Gravitational lens ; you'll need to merge your material in to the Gravitational lens page.

80. GeoN-Kazan-2003 Welcome A special role in the history of the University was played by the great mathematicianNikolai lobachevsky who was Rector of the University from 1827 to 1846. http://www.kcn.ru/tat_ru/universitet/conf/geon/welcome/welcome.html

Welcome Organizing Committees of the Joint International Scientific Conference "Geometry of Nature 2003" extend a warm welcome to all participants and their guests. We wish you a very pleasant stay in Kazan. The Conference is open to all scientists interested. The Conference will give a broad outlook of scientific areas: geometrical, analytical, qualitative, bifurcation and structure analysis of Nature on micro-, meso- and large scales; dynamical systems, resonant structures and natural rhythms; fundamental physics from ground and space, grand unification theory, discrete models, quantum optics, physical cosmology, pulsar astronomy, micro-arcsecond astrometry, extrasolar planet systems; physics, dynamics and chemistry of the Earth, Moon, planets, comets, small bodies; geological budget of planetary rotation, plume and plate tectonics, generation of magnetic fields and surface magnetic anomalies; marine biology, decoding of the genome, genetic and molecular basement of adaptive reaction in living systems, effects of microgravitation; modern ground observations, space missions and future prospective. Joint International Scientific Conference "GeoN-Kazan-2003" hosted and organized by Kazan State University, Russian Ministry of Education, Ministry of Industry, Science and Technology of the Russian Federation, Russian Academy of Sciences, Academy of Science of Tatarstan, Russian Foundation for Basic Research.

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